The Online Virtual Shopping Marketing Essay

The Online Virtual Shopping Marketing Essay Since the development of the Internet, especially in recent times, most of our daily activities are conducted over the internet and goods and services are bought at the click of a mouse. Increasingly, consumers are choosing to make purchases using the Internet and skipping the trip to the store. A modern consumer may purchase a CD player, a couch, groceries, e-books, movies, tickets, software or even a new car at 4.00am without having to leave his or her house, deal with traffic and salespeople, or even change out of her pajamas. Furthermore, a consumer is no longer restricted to products available in one store, one town, or even one country because the Internet transcends boundaries and is literally accessible from anywhere in the world. The Internet essentially is a global network of connections and has become the worlds fastest growing commercial market place. It has developed into a significant and accepted business standard through which consumers and businesses come together in the buying and selling process. Most firms and businesses today have incorporated the concept of e-commerce at some level of their operations and this includes some traditional companies who have now integrated the internet into their businesses. As such, many physical retail stores have expanded their market through the Internet, by having both a virtual store and a physical store, guaranteeing them the best of both worlds. High-volume websites, such as Yahoo!, Amazon.com and eBay, also offer hosting services for online stores, to all retailers for their products and services. These stores are presented as part of an integrated navigation framework. These collections of online stores are sometimes known as virtual shopping malls or onlin e marketplaces. These online marketplaces provide a one stop shop for consumers to shop at their convenience for all the goods that they need. According to a Forrester Research, Understanding Online Shopper Behaviors, US 2011, May 17, 2011, E-commerce Business to Consumer (B2C) product sales totaled $142.5 billion, representing about 8% of retail product sales in the United States. The $26 billion worth of clothes sold online represented about 13% of the domestic market, and with 72% of women looking online for clothing, it has become one of the most popular cross-shopping categories. Forrester Research estimates that the United States online retail industry will be worth $279 billion in 2015. see Forrester: Online Retail Industry In The US Will Be Worth $279 Billion In 2015, TechCrunch. February 28, 2011. Online shopping has become a very popular way of purchasing goods for consumers. All that is required for the consumer is a computer, internet access and a method of payment. The main attractions in shopping for goods on the internet include the opportunity to search for various goods and services, compare the prices offered by various shops, read reviews made by customers who have purchased the same goods or service, order and pay for them and have them delivered, all from the comfort of ones home. Other attractions include the cooling-off period which applies to most online purchases, discounts, promotions and freedom from being pressurised by a salesperson into buying expensive (sometimes unwanted) extended warranties. In other words, customers are attracted to online shopping not only because of the high level of convenience, but also because of the broader selection, competitive pricing, and greater access to information. In comparison with conventional retail shopping, the info rmation environment of virtual/online shopping is improved by providing additional product information such as relative products and services, a choice of alternatives and attributes of each alternative, as well as the reviews and comments by those who have bought or used those goods. This equips the buyer with more information to make a more informed decision. The Nielsen Company conducted a survey, in March 2010 which polled more than 27,000 Internet users in 55 markets from the Asia-Pacific, Europe, Middle East, North America and South America to look at questions such as How do consumers shop online?, What do they intend to buy?, How do they use various online shopping web pages?, and the impact of social media and other factors that come into play when consumers are trying to decide how to spend their money on which product or service. According to that research, reviews on electronics (57%) such as DVD players, cell phones or PlayStations and so on, reviews on cars (45%), and reviews on software (37%) play an important role and have influence on consumers who tend to make purchases and buy these goods online. In addition to online reviews, peer recommendations on the online shopping pages or social networks play a key role for online shoppers while researching future purchases of electronics, cars and travel or concert bookings. See Bonsoni.com on July 10, 2011 (2011-07-10). Research shows word of mouth drives online sales. Bonsoni.com. On the other hand, according to Nielsen Global Online Shopping Report. Blog.nielsen.com. 2010-06-29, 40% of online shoppers indicate that they would not even buy electronics without consulting online reviews first. However, despite the convenience and ease offered by online shopping, there is always the potential for abuse. Arguably the anonymity afforded by the internet has done much to damage the level of trust consumers are willing to place in it, g iven that the internet has no boundaries, and a consumer can access goods and services from any part of the world. According to Proffessor Ian Lloyd in Lloyd I.J. Information Technology law (2008) fifith edition Oxford, pg 483, The Global Top level Domain name .com gives no indication where a business is located and even where the name uses a country code such as .de or .uk, there is no guarantee that the undertaking is established in that country. It is relatively common practice, based in part upon security concerns to keep web servers geographically separate from the physical undertaking. Therefore a website may, for example have an address in German (.de) (or in Hong Kong (.hk), but its owner however might be a United Kingdom-registered compa ny. Furthermore, one of the differences between distance buying and the traditional forms of buying is that there are no face to face interactions between the contracting parties and the goods are not inspected physically by the consumer. Consequently, consumers may find that the goods are faulty on delivery, a wrong order or that the goods are not the correct specifications. Consumers are therefore concerned with the ease with which they can return an item for the correct one or for a refund.  To improve confidence, business often attempt to adopt online shopping techniques which are user-centred. They describe goods with photos, texts and multimedia files, provide background information, advice, or how-to guides designed to help consumers decide which product to buy and provide link to supplemental product information, such as instructions, safety procedures, demonstrations, or manufacturer specifications. Also they provide for ease of return and refunds by providing information to c ustomers on how to return goods for refund or exchange. Some customers on their own part now refer to show rooming before purchasing online. By this, customers first inspect the goods in the shops before purchasing them online. Furthermore, most laws on E-commerce make provision for the protection of the consumer in online contracts. Other problems that undermine consumers confidence in online shopping includes Fraud and security concerns. These include identity theft, phishing, denial of Service attacks etc. The perpetrators get hold of consumers credit card information and use it to commit fraud. To combat this, most online businesses adopt encryption on their websites as well as other security measures to prevent fraudsters from getting hold of customers information. The use of Paypal accounts are also useful in securing against fraud on the Internet. Other disadvantages of online shopping include lack of full cost disclosure and Data protection. In conclusion, the trend of shopping online has come to stay. Online shops are open 24 hours of the day and can be accessed from anywhere where there is an internet connection. The ease and convenience of shopping online will always lure more consumers to it. However, consumers must be alert and aware of the risks involved and take extra care when shopping online. Due to the openness and competitiveness of the online market, most business will always strive to maintain the highest standard of security as well as a user centred website to boost their business.

Grades Encourage Students to Learn Essay

These days there are a lot of discussions over education in many colleges and universities. One of the matters under consideration is whether grades encourage students to learn. Some people think that students are not encouraged to learn by grades. From my point of view, I believe that marks actually stimulate students to study for the three following reasons: First of all, grade obviously is a good way to estimate students. If a student gets a good mark, he could feel proud of this result. Moreover, he could be praised for his studiousness as well as intelligence by his teacher and parents and get admiration from his friends. As a result, he would try his best to get at least the same grade in the next time. On the contrary, students getting bad grades would give their whole mind on to their study so as to get higher grades and not be dropped back. In short, grades motivate students to learn much more just because they are supposed as a mirror reflecting students’ performances. Second, grade could enable students clearly understand their performance as well as help them become aware of their strengths and weaknesses. For instance, when I was in high school, I always got good marks in English tests and I realized that I had an aptitude for English. So I decided to choose English as my major at Huflit university. And now, I always get good grades, even excellent ones in English. This makes me feel satisfied with my choice. I will also choose a job as teacher of English after graduating from the university. If there had not been grades, I think I wouldn’t have known what major really suitable for me and I would not be pleased with my present major. So, grade plays an essential role in students’ study. Furthermore, students with good grades could easily reach their dreams in study and career. They have more opportunities to get noble rewards in the national as well as international examinations. Also, attending prestigious universities would become easy for them. This will help heighten their job and promotion opportunities after graduating form those universities especially in today’s ompetitive labor market. For this reason, students always try to get high grades to gain a lot of advantages in their lives. In short, grade actually encourages students to learn much more simply because students are not only evaluated by grades, but also know clearly their strong and weak points. And specially, students with good marks could have much more chances to achieve success in life. So, there is a question for all of us: â€Å"What would happen to students if there was not grade? †

Sensitivity Analysis

Linear Programming Notes VII Sensitivity Analysis 1 Introduction When you use a mathematical model to describe reality you must make approximations. The world is more complicated than the kinds of optimization problems that we are able to solve. Linearity assumptions usually are signi? cant approximations. Another important approximation comes because you cannot be sure of the data that you put into the model. Your knowledge of the relevant technology may be imprecise, forcing you to approximate values in A, b, or c. Moreover, information may change.Sensitivity analysis is a systematic study of how sensitive (duh) solutions are to (small) changes in the data. The basic idea is to be able to give answers to questions of the form: 1. If the objective function changes, how does the solution change? 2. If resources available change, how does the solution change? 3. If a constraint is added to the problem, how does the solution change? One approach to these questions is to solve lots of l inear programming problems. For example, if you think that the price of your primary output will be between $100 and $120 per unit, you can solve twenty di? rent problems (one for each whole number between $100 and $120). 1 This method would work, but it is inelegant and (for large problems) would involve a large amount of computation time. (In fact, the computation time is cheap, and computing solutions to similar problems is a standard technique for studying sensitivity in practice. ) The approach that I will describe in these notes takes full advantage of the structure of LP programming problems and their solution. It turns out that you can often ? gure out what happens in â€Å"nearby† linear programming problems just by thinking and by examining the information provided by the simplex algorithm.In this section, I will describe the sensitivity analysis information provided in Excel computations. I will also try to give an intuition for the results. 2 Intuition and Overvie w Throughout these notes you should imagine that you must solve a linear programming problem, but then you want to see how the answer changes if the problem is changed. In every case, the results assume that only one thing about the problem changes. That is, in sensitivity analysis you evaluate what happens when only one parameter of the problem changes. 1 OK, there are really 21 problems, but who is counting? 1To ? x ideas, you may think about a particular LP, say the familiar example: max 2Ãâ€"1 subject to 3Ãâ€"1 x1 2x 1 + + + 4Ãâ€"2 x2 3Ãâ€"2 x2 + + + + 3x 3 x3 2x 3 3x 3 + + + x4 4x 4 3x 4 x4 x ? ? ? 12 7 10 0 We know that the solution to this problem is x0 = 42, x1 = 0; x2 = 10. 4; x3 = 0; x4 = . 4. 2. 1 Changing Objective Function Suppose that you solve an LP and then wish to solve another problem with the same constraints but a slightly di? erent objective function. (I will always make only one change in the problem at a time. So if I change the objective function, not onl y will I hold the constraints ? ed, but I will change only one coe cient in the objective function. ) When you change the objective function it turns out that there are two cases to consider. The ? rst case is the change in a non-basic variable (a variable that takes on the value zero in the solution). In the example, the relevant non-basic variables are x1 and x3 . What happens to your solution if the coe cient of a non-basic variable decreases? For example, suppose that the coe cient of x1 in the objective function above was reduced from 2 to 1 (so that the objective function is: max x1 + 4Ãâ€"2 + 3Ãâ€"3 + x4 ).What has happened is this: You have taken a variable that you didn’t want to use in the ? rst place (you set x1 = 0) and then made it less pro? table (lowered its coe cient in the objective function). You are still not going to use it. The solution does not change. Observation If you lower the objective function coe cient of a non-basic variable, then the solution does not change. What if you raise the coe cient? Intuitively, raising it just a little bit should not matter, but raising the coe cient a lot might induce you to change the value of x in a way that makes x1 > 0.So, for a non-basic variable, you should expect a solution to continue to be valid for a range of values for coe cients of nonbasic variables. The range should include all lower values for the coe cient and some higher values. If the coe cient increases enough (and putting the variable into the basis is feasible), then the solution changes. What happens to your solution if the coe cient of a basic variable (like x2 or x4 in the example) decreases? This situation di? ers from the previous one in that you are using the basis variable in the ? rst place. The change makes the variable contribute less to pro? . You should expect that a su ciently large reduction makes you want to change your solution (and lower the value the associated variable). For example, if the coe cient of x2 in the objective function in the example were 2 instead of 4 (so that the objective was max 2Ãâ€"1 +2Ãâ€"2 +3Ãâ€"3 + x4 ), 2 maybe you would want to set x2 = 0 instead of x2 = 10. 4. On the other hand, a small reduction in x2 ’s objective function coe cient would typically not cause you to change your solution. In contrast to the case of the non-basic variable, such a change will change the value of your objective function.You compute the value by plugging in x into the objective function, if x2 = 10. 4 and the coe cient of x2 goes down from 4 to 2, then the contribution of the x2 term to the value goes down from 41. 6 to 20. 8 (assuming that the solution remains the same). If the coe cient of a basic variable goes up, then your value goes up and you still want to use the variable, but if it goes up enough, you may want to adjust x so that it x2 is even possible. In many cases, this is possible by ? nding another basis (and therefore another solution).So, intuitively, t here should be a range of values of the coe cient of the objective function (a range that includes the original value) in which the solution of the problem does not change. Outside of this range, the solution will change (to lower the value of the basic variable for reductions and increase its value of increases in its objective function coe cient). The value of the problem always changes when you change the coe cient of a basic variable. 2. 2 Changing a Right-Hand Side Constant We discussed this topic when we talked about duality. I argued that dual prices capture the e? ct of a change in the amounts of available resources. When you changed the amount of resource in a non-binding constraint, then increases never changed your solution. Small decreases also did not change anything, but if you decreased the amount of resource enough to make the constraint binding, your solution could change. (Note the similarity between this analysis and the case of changing the coe cient of a non-bas ic variable in the objective function. Changes in the right-hand side of binding constraints always change the solution (the value of x must adjust to the new constraints).We saw earlier that the dual variable associated with the constraint measures how much the objective function will be in? uenced by the change. 2. 3 Adding a Constraint If you add a constraint to a problem, two things can happen. Your original solution satis? es the constraint or it doesn’t. If it does, then you are ? nished. If you had a solution before and the solution is still feasible for the new problem, then you must still have a solution. If the original solution does not satisfy the new constraint, then possibly the new problem is infeasible. If not, then there is another solution.The value must go down. (Adding a constraint makes the problem harder to satisfy, so you cannot possibly do better than before). If your original solution satis? es your new constraint, then you can do as well as before. I f not, then you will do worse. 2 2 There is a rare case in which originally your problem has multiple solutions, but only some of them satisfy the added constraint. In this case, which you need not worry about, 3 2. 4 Relationship to the Dual The objective function coe cients correspond to the right-hand side constants of resource constraints in the dual.The primal’s right-hand side constants correspond to objective function coe cients in the dual. Hence the exercise of changing the objective function’s coe cients is really the same as changing the resource constraints in the dual. It is extremely useful to become comfortable switching back and forth between primal and dual relationships. 3 Understanding Sensitivity Information Provided by Excel Excel permits you to create a sensitivity report with any solved LP. The report contains two tables, one associated with the variables and the other associated with the constraints.In reading these notes, keep the information i n the sensitivity tables associated with the ? rst simplex algorithm example nearby. 3. 1 Sensitivity Information on Changing (or Adjustable) Cells The top table in the sensitivity report refers to the variables in the problem. The ? rst column (Cell) tells you the location of the variable in your spreadsheet; the second column tells you its name (if you named the variable); the third column tells you the ? nal value; the fourth column is called the reduced cost; the ? fth column tells you the coe cient in the problem; the ? al two columns are labeled â€Å"allowable increase† and â€Å"allowable decrease. † Reduced cost, allowable increase, and allowable decrease are new terms. They need de? nitions. The allowable increases and decreases are easier. I will discuss them ? rst. The allowable increase is the amount by which you can increase the coe cient of the objective function without causing the optimal basis to change. The allowable decrease is the amount by which y ou can decrease the coe cient of the objective function without causing the optimal basis to change. Take the ? rst row of the table for the example. This row describes the variable x1 .The coe cient of x1 in the objective function is 2. The allowable increase is 9, the allowable decrease is â€Å"1. 00E+30,† which means 1030 , which really means 1. This means that provided that the coe cient of x1 in the objective function is less than 11 = 2 + 9 = original value + allowable increase, the basis does not change. Moreover, since x1 is a non-basic variable, when the basis stays the same, the value of the problem stays the same too. The information in this line con? rms the intuition provided earlier and adds something new. What is con? rmed is that if you lower the objective coe cient of a non-basic ariable, then your solution does not change. (This means that the allowable decrease will always be in? nite for a non-basic variable. ) The example also demonstrates your value wil l stay the same. 4 that increasing the coe cient of a non-basic variable may lead to a change in basis. In the example, if you increase the coe cient of x1 from 2 to anything greater than 9 (that is, if you add more than the allowable increase of 7 to the coe cient), then you change the solution. The sensitivity table does not tell you how the solution changes, but common sense suggests that x1 will take on a positive value.Notice that the line associated with the other non-basic variable of the example, x3 , is remarkably similar. The objective function coe cient is di? erent (3 rather than 2), but the allowable increase and decrease are the same as in the row for x1 . It is a coincidence that the allowable increases are the same. It is no coincidence that the allowable decrease is the same. We can conclude that the solution of the problem does not change as long as the coe cient of x3 in the objective function is less than or equal to 10. Consider now the basic variables. For x2 t he allowable increase is in? ite 9 while the allowable decrease is 2. 69 (it is 2 13 to be exact). This means that if the solution won’t change if you increase the coe cient of x2 , but it will change if you decrease the coe cient enough (that is, by more than 2. 7). The fact that your solution does not change no matter how much you increase x2 ’s coe cient means that there is no way to make x2 > 10. 4 and still satisfy the constraints of the problem. The fact that your solution does change when you increase x2 ’s coe cient by enough means that there is a feasible basis in which x2 takes on a value lower than 10. 4. You knew that. Examine the original basis for the problem. ) The range for x4 is di? erent. Line four of the sensitivity table says that the solution of the problem does not change provided that the coe cient of x4 in the objective function stays between 16 (allowable increase 15 plus objective function coe cient 1) and -4 (objective function coe cie nt minus allowable decrease). That is, if you make x4 su ciently more attractive, then your solution will change to permit you to use more x4 . If you make x4 su ciently less attractive the solution will also change. This time to use less x4 .Even when the solution of the problem does not change, when you change the coe cient of a basic variable the value of the problem will change. It will change in a predictable way. Speci? cally, you can use the table to tell you the solution of the LP when you take the original constraints and replace the original objective function by max 2Ãâ€"1 + 6Ãâ€"2 + 3Ãâ€"3 + x4 (that is, you change the coe cient of x2 from 4 to 6), then the solution to the problem remains the same. The value of the solution changes because now you multiply the 10. 4 units of x2 by 6 instead of 4. The objective function therefore goes up by 20. . The reduced cost of a variable is the smallest change in the objective function coe cient needed to arrive at a solution in which the variable takes on a positive value when you solve the problem. This is a mouthful. Fortunately, reduced costs are redundant information. The reduced cost is the negative of the allowable increase for non-basic variables (that is, if you change the coe cient of x1 by 7, then you arrive at a problem in which x1 takes on a positive 5 value in the solution). This is the same as saying that the allowable increase in the coe cient is 7.The reduced cost of a basic variable is always zero (because you need not change the objective function at all to make the variable positive). Neglecting rare cases in which a basis variable takes on the value 0 in a solution, you can ? gure out reduced costs from the other information in the table: If the ? nal value is positive, then the reduced cost is zero. If the ? nal value is zero, then the reduced cost is negative one times the allowable increase. Remarkably, the reduced cost of a variable is also the amount of slack in the dual constraint associated with the variable.With this interpretation, complementary slackness implies that if a variable that takes on a positive value in the solution, then its reduced cost is zero. 3. 2 Sensitivity Information on Constraints The second sensitivity table discusses the constraints. The cell column identi? es the location of the left-hand side of a constraint; the name column gives its name (if any); the ? nal value is the value of the left-hand side when you plug in the ? nal values for the variables; the shadow price is the dual variable associated with the constraint; the constraint R. H. ide is the right hand side of the constraint; allowable increase tells you by how much you can increase the right-hand side of the constraint without changing the basis; the allowable decrease tells you by how much you can decrease the right-hand side of the constraint without changing the basis. Complementary Slackness guarantees a relationship between the columns in the constraint table. The di? erence between the â€Å"Constraint Right-Hand Side† column and the â€Å"Final Value† column is the slack. (So, from the table, the slack for the three constraints is 0 (= 12 12), 37 (= 7 ( 30)), and 0 (= 10 10), respectively.We know from Complementary Slackness that if there is slack in the constraint then the associated dual variable is zero. Hence CS tells us that the second dual variable must be zero. Like the case of changes in the variables, you can ? gure out information on allowable changes from other information in the table. The allowable increase and decrease of non-binding variables can be computed knowing ? nal value and right-hand side constant. If a constraint is not binding, then adding more of the resource is not going to change your solution. Hence the allowable increase of a resource is in? ite for a non-binding constraint. (A nearly equivalent, and also true, statement is that the allowable increase of a resource is in? nite for a constraint w ith slack. ) In the example, this explains why the allowable increase of the second constraint is in? nite. One other quantity is also no surprise. The allowable decrease of a non-binding constraint is equal to the slack in the constraint. Hence the allowable decrease in the second constraint is 37. This means that if you decrease the right-hand side of the second constraint from its original value (7) to nything greater than 30 you do not change the optimal basis. In fact, the only part of the solution that changes when you do this is that the value of the slack variable for this constraint changes. In this paragraph, the point is only this: If you solve an LP and ? nd that a constraint is not binding, 6 then you can remove all of the unused (slack) portion of the resource associated with this constraint and not change the solution to the problem. The allowable increases and decreases for constraints that have no slack are more complicated. Consider the ? rst constraint.The informa tion in the table says that if the right-hand side of the ? rst constraint is between 10 (original value 12 minus allowable decrease 2) and in? nity, then the basis of the problem does not change. What these columns do not say is that the solution of the problem does change. Saying that the basis does not change means that the variables that were zero in the original solution continue to be zero in the new problem (with the right-hand side of the constraint changed). However, when the amount of available resource changes, necessarily the values of the other variables change. You can think about this in many ways. Go back to a standard example like the diet problem. If your diet provides exactly the right amount of Vitamin C, but then for some reason you learn that you need more Vitamin C. You will certainly change what you eat and (if you aren’t getting your Vitamin C through pills supplying pure Vitamin C) in order to do so you probably will need to change the composition of your diet – a little more of some foods and perhaps less of others. I am saying that (within the allowable range) you will not change the foods that you eat in positive amounts.That is, if you ate only spinach and oranges and bagels before, then you will only eat these things (but in di? erent quantities) after the change. Another thing that you can do is simply re-solve the LP with a di? erent right-hand side constant and compare the result. To ? nish the discussion, consider the third constraint in the example. The values for the allowable increase and allowable decrease guarantee that the basis that is optimal for the original problem (when the right-hand side of the third constraint is equal to 10) remains obtain provided that the right-hand side constant in this constraint is between -2. 333 and 12. Here is a way to think about this range. Suppose that your LP involves four production processes and uses three basic ingredients. Call the ingredients land, labor, and capi tal. The outputs vary use di? erent combinations of the ingredients. Maybe they are growing fruit (using lots of land and labor), cleaning bathrooms (using lots of labor), making cars (using lots of labor and and a bit of capital), and making computers (using lots of capital). For the initial speci? cation of available resources, you ? nd that your want to grow fruit and make cars.If you get an increase in the amount of capital, you may wish to shift into building computers instead of cars. If you experience a decrease in the amount of capital, you may wish to shift away from building cars and into cleaning bathrooms instead. As always when dealing with duality relationships, the the â€Å"Adjustable Cells† table and the â€Å"Constraints† table really provide the same information. Dual variables correspond to primal constraints. Primal variables correspond to dual constraints. Hence, the â€Å"Adjustable Cells† table tells you how sensitive primal variables and dual constraints are to changes in the primal objective function.The â€Å"Constraints† table tells you how sensitive dual variables and primal constraints are to changes in the dual objective function (right-hand side constants in the primal). 7 4 Example In this section I will present another formulation example and discuss the solution and sensitivity results. Imagine a furniture company that makes tables and chairs. A table requires 40 board feet of wood and a chair requires 30 board feet of wood. Wood costs $1 per board foot and 40,000 board feet of wood are available. It takes 2 hours of skilled labor to make an un? nished table or an un? ished chair. Three more hours of labor will turn an un? nished table into a ? nished table; two more hours of skilled labor will turn an un? nished chair into a ? nished chair. There are 6000 hours of skilled labor available. (Assume that you do not need to pay for this labor. ) The prices of output are given in the table below: Produ ct Un? nished Table Finished Table Un? nished Chair Finished Chair Price $70 $140 $60 $110 We want to formulate an LP that describes the production plans that the ? rm can use to maximize its pro? ts. The relevant variables are the number of ? nished and un? ished tables, I will call them TF and TU , and the number of ? nished and un? nished chairs, CF and CU . The revenue is (using the table): 70TU + 140TF + 60CU + 110CF , , while the cost is 40TU + 40TF + 30CU + 30CF (because lumber costs $1 per board foot). The constraints are: 1. 40TU + 40TF + 30CU + 30CF ? 40000. 2. 2TU + 5TF + 2CU + 4CF ? 6000. The ? rst constraint says that the amount of lumber used is no more than what is available. The second constraint states that the amount of labor used is no more than what is available. Excel ? nds the answer to the problem to be to construct only ? nished chairs (1333. 33 – I’m not sure what it means to make a sell 1 chair, but let’s assume 3 that this is possible) . The pro? t is $106,666. 67. Here are some sensitivity questions. 1. What would happen if the price of un? nished chairs went up? Currently they sell for $60. Because the allowable increase in the coe cient is $50, it would not be pro? table to produce them even if they sold for the same amount as ? nished chairs. If the price of un? nished chairs went down, then certainly you wouldn’t change your solution. 8 2. What would happen if the price of un? nished tables went up? Here something apparently absurd happens.The allowable increase is greater than 70. That is, even if you could sell un? nished tables for more than ? nished tables, you would not want to sell them. How could this be? The answer is that at current prices you don’t want to sell ? nished tables. Hence it is not enough to make un? nished tables more pro? table than ? nished tables, you must make them more pro? table than ? nished chairs. Doing so requires an even greater increase in the price. 3. What if the price of ? nished chairs fell to $100? This change would alter your production plan, since this would involve a $10 decrease in the price of ? ished chairs and the allowable decrease is only $5. In order to ? gure out what happens, you need to re-solve the problem. It turns out that the best thing to do is specialize in ? nished tables, producing 1000 and earning $100,000. Notice that if you continued with the old production plan your pro? t would be 70 ? 1333 1 = 93, 333 1 , so the change in production plan 3 3 was worth more than $6,000. 4. How would pro? t change if lumber supplies changed? The shadow price of the lumber constraint is $2. 67. The range of values for which the basis remains unchanged is 0 to 45,000.This means that if the lumber supply went up by 5000, then you would continue to specialize in ? nished chairs, and your pro? t would go up by $2. 67 ? 5000 = $10, 333. At this point you presumably run out of labor and want to reoptimize. If lumber supply decreased , then your pro? t would decrease, but you would still specialize in ? nished chairs. 5. How much would you be willing to pay an additional carpenter? Skilled labor is not worth anything to you. You are not using the labor than you have. Hence, you would pay nothing for additional workers. 6. Suppose that industrial regulations complicate the ? ishing process, so that it takes one extra hour per chair or table to turn an un? nished product into a ? nished one. How would this change your plans? You cannot read your answer o? the sensitivity table, but a bit of common sense tells you something. The change cannot make you better o?. On the other hand, to produce 1,333. 33 ? nished chairs you’ll need 1,333. 33 extra hours of labor. You do not have that available. So the change will change your pro? t. Using Excel, it turns out that it becomes optimal to specialize in ? nished tables, producing 1000 of them and earning $100,000. This problem di? ers from the original one because t he amount of labor to create a ? nished product increases by one unit. ) 7. The owner of the ? rm comes up with a design for a beautiful hand-crafted cabinet. Each cabinet requires 250 hours of labor (this is 6 weeks of full time work) and uses 50 board feet of lumber. Suppose that the company can sell a cabinet for $200, would it be worthwhile? You could solve this 9 problem by changing the problem and adding an additional variable and an additional constraint. Note that the coe cient of cabinets in the objective function is 150, which re? cts the sale price minus the cost of lumber. I did the computation. The ? nal value increased to 106,802. 7211. The solution involved reducing the output of un? nished chairs to 1319. 727891 and increasing the output of cabinets to 8. 163265306. (Again, please tolerate the fractions. ) You could not have guessed these ? gures in advance, but you could ? gure out that making cabinets was a good idea. The way to do this is to value the inputs to th e production of cabinets. Cabinets require labor, but labor has a shadow price of zero. They also require lumber. The shadow price of lumber is $2. 7, which means that each unit of lumber adds $2. 67 to pro? t. Hence 50 board feet of lumber would reduce pro? t by $133. 50. Since this is less than the price at which you can sell cabinets (minus the cost of lumber), you are better o? using your resources to build cabinets. (You can check that the increase in pro? t associated with making cabinets is $16. 50, the added pro? t per unit, times the number of cabinets that you actually produce. ) I attached a sheet where I did the same computation assuming that the price of cabinets was $150. In this case, the additional option does not lead to cabinet production. 10

Liberal Democracy and Capitalism after World War 1 - Free Essay Example

Sample details Pages: 2 Words: 490 Downloads: 2 Date added: 2019/02/15 Category Politics Essay Level High school Tags: Democracy Essay Did you like this example? The aftermath of the First World War proved it difficult for capitalism to be transformed into socialism in and peaceful way. A new ideology found its way in driving the world economy to respond to the changing economic and political spectrum that Britain and its empire was embedded. Capitalist competition was increasing amongst the states and their colonies. Don’t waste time! Our writers will create an original "Liberal Democracy and Capitalism after World War 1" essay for you Create order The nations were not only in need for a strong economy and political power but there was great scramble for military strength. The lessons learned from the First World War saw states struggling to have more advantage against their rivalry states (Bowles Gintis, 2008). Despite the fact that the war was over, there was seemingly an atmosphere suggesting that a cold war was taking place. This undermined would definitely undermine efforts for liberal democracy because the capitalist did not want to engage the rival states. The representative governments faced challenges of democratization since nations that would they would wish to engage in diplomatic relations appeared to be more concerned about their military strength for fear of another war. The wounds of the past events were still fresh. The treaties were singed to enhance democracy although some of the treaties like the treaty of versatile appeared to have affected Germany the hard way (Bowles Gintis, 2008). As a result, the diplomatic relations between Germany and its allied powers with the rest of Europe was ruined is one the major causes of the Second World War. Despite the fact that the treaty ended the war, it changed diplomatic ties between nations and created a cold war atmosphere in the European world. The aftermath of the WWI greatly affected the economy of the representative governments lowering their determination. Capitalism dominated the economically affected nations alike Germany and Britain and for the purposes of restring their e conomic status (Hicks, 2009). Liberal democracy was suppressed and diplomacy way silently exercised. The failure of economic systems threatened the stability of the European governments because the source of finance for military strength was from their stable economy. A failed economy exposed them to threats of attack if another war broke out. Since the stability of governments was marked by its economy, the risk of disasters such as hunger and diseases was a great worry for the affected states. The challenges in governorship undermined the global order of events with a shift in states that were much powerful (Hicks, 2009).The global error of colonialism gained much strength as colonialists gained much entry and control of their colonies in efforts to recover from a period of massive destruction. The nations that felt stronger wanted to rule the world by being superpowers. The Soviet Union and Britain were perceived to be stronger than any other nation in the world. Some of the challenges that the governments at this juncture faced were being attributed to selfishness of the leaders . There arose dictatorial leaders like Hitler who wanted to establish a certain world order in their countries.