Solve in 20 minutes and get the thumb up please QListenDorian Auto manufacturers luxury cars and trucks. The company believes that itsmost likely customers are high-income women and men. To reach these groups,Dorian Auto has embarked on a ambitious TV advertising campaign and has decidedto purchase 1-minute commercial spots on two types of programs; comedy showsand football games. Each comedy commercial is seen by 7 million high incomewomen and 2 million high income men. Each football commercial is seen by 3 millionhigh-income women and 11 million high-income men. A 1-minute comedy ad costs$40,000, and a 1-minute football ad costs $90,000. Dorian would like thecommercials to be seen by at least 25 million high-income women and 20 millionhigh-income men.Use linear programming to determine how Dorian Auto can meet its advertisingrequirements at minimum cost.

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Answered: Dorian Auto manufacturers luxury cars…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 47P

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The eTech Company is a fairly recent entry in the electronic device area. The company competes with Apple. Samsung, and other well-known companies in the manufacturing and sales of personal handheld devices. Although eTech recognizes that it is a niche player and will likely remain so in the foreseeable future, it is trying to increase its current small market share in this huge competitive market. Jim Simons, VP of Production, and Catherine Dolans, VP of Marketing, have been discussing the possible addition of a new product to the companys current (rather limited) product line. The tentative name for this new product is ePlayerX. Jim and Catherine agree that the ePlayerX, which will feature a sleeker design and more memory, is necessary to compete successfully with the big boys, but they are also worried that the ePlayerX could cannibalize sales of their existing productsand that it could even detract from their bottom line. They must eventually decide how much to spend to develop and manufacture the ePlayerX and how aggressively to market it. Depending on these decisions, they must forecast demand for the ePlayerX, as well as sales for their existing products. They also realize that Apple. Samsung, and the other big players are not standing still. These competitors could introduce their own new products, which could have very negative effects on demand for the ePlayerX. The expected timeline for the ePlayerX is that development will take no more than a year to complete and that the product will be introduced in the market a year from now. Jim and Catherine are aware that there are lots of decisions to make and lots of uncertainties involved, but they need to start somewhere. To this end. Jim and Catherine have decided to base their decisions on a planning horizon of four years, including the development year. They realize that the personal handheld device market is very fluid, with updates to existing products occurring almost continuously. However, they believe they can include such considerations into their cost, revenue, and demand estimates, and that a four-year planning horizon makes sense. In addition, they have identified the following problem parameters. (In this first pass, all distinctions are binary: low-end or high-end, small-effect or large-effect, and so on.) In the absence of cannibalization, the sales of existing eTech products are expected to produce year I net revenues of 10 million, and the forecast of the annual increase in net revenues is 2%. The ePIayerX will be developed as either a low-end or a high-end product, with corresponding fixed development costs (1.5 million or 2.5 million), variable manufacturing costs ( 100 or 200). and selling prices (150 or 300). The fixed development cost is incurred now, at the beginning of year I, and the variable cost and selling price are assumed to remain constant throughout the planning horizon. The new product will be marketed either mildly aggressively or very aggressively, with corresponding costs. The costs of a mildly aggressive marketing campaign are 1.5 million in year 1 and 0.5 million annually in years 2 to 4. For a very aggressive campaign, these costs increase to 3.5 million and 1.5 million, respectively. (These marketing costs are not part of the variable cost mentioned in the previous bullet; they are separate.) Depending on whether the ePlayerX is a low-end or high-end produce the level of the ePlayerXs cannibalization rate of existing eTech products will be either low (10%) or high (20%). Each cannibalization rate affects only sales of existing products in years 2 to 4, not year I sales. For example, if the cannibalization rate is 10%, then sales of existing products in each of years 2 to 4 will be 10% below their projected values without cannibalization. A base case forecast of demand for the ePlayerX is that in its first year on the market, year 2, demand will be for 100,000 units, and then demand will increase by 5% annually in years 3 and 4. This base forecast is based on a low-end version of the ePlayerX and mildly aggressive marketing. It will be adjusted for a high-end will product, aggressive marketing, and competitor behavior. The adjustments with no competing product appear in Table 2.3. The adjustments with a competing product appear in Table 2.4. Each adjustment is to demand for the ePlayerX in each of years 2 to 4. For example, if the adjustment is 10%, then demand in each of years 2 to 4 will be 10% lower than it would have been in the base case. Demand and units sold are the samethat is, eTech will produce exactly what its customers demand so that no inventory or backorders will occur. Table 2.3 Demand Adjustments When No Competing Product Is Introduced Table 2.4 Demand Adjustments When a Competing Product Is Introduced Because Jim and Catherine are approaching the day when they will be sharing their plans with other company executives, they have asked you to prepare an Excel spreadsheet model that will answer the many what-if questions they expect to be asked. Specifically, they have asked you to do the following: You should enter all of the given data in an inputs section with clear labeling and appropriate number formatting. If you believe that any explanations are required, you can enter them in text boxes or cell comments. In this section and in the rest of the model, all monetary values (other than the variable cost and the selling price) should be expressed in millions of dollars, and all demands for the ePlayerX should be expressed in thousands of units. You should have a scenario section that contains a 0/1 variable for each of the binary options discussed here. For example, one of these should be 0 if the low-end product is chosen and it should be 1 if the high-end product is chosen. You should have a parameters section that contains the values of the various parameters listed in the case, depending on the values of the 0/1 variables in the previous bullet For example, the fixed development cost will be 1.5 million or 2.5 million depending on whether the 0/1 variable in the previous bullet is 0 or 1, and this can be calculated with a simple IF formula. You can decide how to implement the IF logic for the various parameters. You should have a cash flows section that calculates the annual cash flows for the four-year period. These cash flows include the net revenues from existing products, the marketing costs for ePlayerX, and the net revenues for sales of ePlayerX (To calculate these latter values, it will help to have a row for annual units sold of ePlayerX.) The cash flows should also include depreciation on the fixed development cost, calculated on a straight-line four-year basis (that is. 25% of the cost in each of the four years). Then, these annual revenues/costs should be summed for each year to get net cash flow before taxes, taxes should be calculated using a 32% tax rate, and taxes should be subtracted and depreciation should be added back in to get net cash flows after taxes. (The point is that depreciation is first subtracted, because it is not taxed, but then it is added back in after taxes have been calculated.) You should calculate the company's NPV for the four-year horizon using a discount rate of 10%. You can assume that the fixed development cost is incurred now. so that it is not discounted, and that all other costs and revenues are incurred at the ends of the respective years. You should accompany all of this with a line chart with three series: annual net revenues from existing products; annual marketing costs for ePlayerX; and annual net revenues from sales of ePlayerX. Once all of this is completed. Jim and Catherine will have a powerful tool for presentation purposes. By adjusting the 0/1 scenario variables, their audience will be able to see immediately, both numerically and graphically, the financial consequences of various scenarios.
The campaign manager for a politician who is running for reelection to a political office is planning the campaign. Four ways to advertise have been selected: TV ads, radio ads, billboards, and social media advertising buys. The costs of these are $900 for each TV ad, $500 for each radio ad, $600 for a billboard for 1 month, and $180 for each buy on social media (approximately 40,000 unique impressions). The audience reached by each type of advertising has been estimated to be 40,000 for each TV ad, 32,000 for each radio ad, 34,000 for each billboard, and 17,000 for each social media buy. The total monthly advertising budget is $16,000. The following goals have been established and ranked: The number of people reached should be at least 1,500,000. The total monthly advertising budget should not be exceeded. Together, the number of ads on either TV or radio should be at least 6. No more than 10 ads/buys of any one type should be used. Formulate this as a goal programming problem. Solve…
A portfolio manager summarizes the input from the macro and micro forecasters in the following table: Micro Forecasts AssetExpected Return (%)BetaResidual Standard Deviation (%) Stock A 22 1.4 53 Stock B 21 1.8 61 Stock C 19 0.7 58 Stock D 16 1.1 46 Macro Forecasts AssetExpected Return (%)Standard Deviation (%) T-bills 7 0 Passive equity portfolio 16 20 Calculate the following for a portfolio manager who is not allowed to short sell securities. If allowed to short sell securities, the manager's Sharpe ratio is 0.4647. a. What is the cost of the restriction in terms of Sharpe’s measure? (Do not round intermediate calculations. Enter your answer as decimals rounded to 4 places.) cost of restriction= b. What is the utility loss to the investor (A = 1.9) given his new complete portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Consider the Answer and Sensitivity Reports at the end of the questionnaire to answer the following questions Objective Function : Max Z = 3x1 +2x2 Sensitivity Ranges : C1 (3) Upper limit 3 +∞ = ∞ Lower limit 3-2 = 1 C2 (2) Upper limit 4+2 = 6 Lower limit 2-3.5 = -1.5 What are the constraint quantity values? Identify the sensitivity ranges for the constraint quantity Are there any unused resources? If so, which ones and what are the amount of unused resources?
The Tennessee Jack Distillery produces custom-blendedwhiskey. A particular blend consists of rye and bourbonwhiskey. The company has received an order for a minimumof 400 gallons of the custom blend. The customer specifiedthat the order must contain at least 40 percent rye and notmore than 250 gallons of bourbon. The customer also speci-fied that the blend should be mixed in the ratio of two partsrye to one part bourbon. The distillery can produce 500 gal-lons per week, regardless of the blend. The production man-ager wants to complete the order in one week. The blend issold for $12 per gallon. The distillery company’s cost pergallon is $4 for rye and $2 for bourbon. The company wantsto determine the blend mix that will meet customer require-ments and maximize profits.a. Formulate and solve a linear programming model forthis problem.b. Solve the problem using the graphical method.
The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $1000 between newspaper advertising and radio advertising. Management decided that at least 25% of the budget must be spent on each type of media, and that the amount of money spent on local newspaper advertising must be at least twice the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from 0 to 100, with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is 50 and the value of the index for spot radio advertising is 80, how should the restaurant allocate its advertising budget in order to maximize the value of total audience exposure? a. Formulate a linear programming model that can be used to determine how the restaurant should allocate its advertising budget in order to maximize the value of total audience exposure. It's…
Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…
A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for 10 Hollywood movies made in the past five years. Each movie was based on an epic novel. For these data, x1 = first-year box office receipts of the movie, x2 = total production costs of the movie, x3 = total promotional costs of the movie, and x4 = total book sales prior to movie release. All units are in millions of dollars. x1 x2 x3 x4 85.1 8.5 5.1 4.7 106.3 12.9 5.8 8.8 50.2 5.2 2.1 15.1 130.6 10.7 8.4 12.2 54.8 3.1 2.9 10.6 30.3 3.5 1.2 3.5 79.4 9.2 3.7 9.7 91.0 9.0 7.6 5.9 135.4 15.1 7.7 20.8 89.3 10.2 4.5 7.9 a) Suppose Hollywood is planning a new epic movie with projected box office sales x1 = 100 million and production costs x2 = 12 million. The book on which the movie is based had sales of x4 = 9.2 million. Forecast the dollar amount (in millions) that should be budgeted for promotion costs x3 and find an 80% confidence interval for your…
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine (grams) L-Glutamine (grams) BCAAs (grams) Xtend(SciVation) 0 2.5 7 Gainz(MP Hardcore) 2 3 6 Strongevity(Bill Phillips) 2.5 1 0 Muscle Physique(EAS) 2 2 0 Your personal trainer suggests that you supplement with as much BCAAs as possible but with no more than 36 grams of creatine and 54 grams of L-glutamine per week. You are thinking of combining Xtend, Gainz, and Strongevity to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications and also includes at least as many servings of Strongevity as Xtend? Xtend servings Gainz servings Strongevity servings How much BCAAs will you obtain? g
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine (grams) L-Glutamine (grams) BCAAs (grams) Xtend(SciVation) 0 2.5 7 Gainz(MP Hardcore) 2 3 6 Strongevity(Bill Phillips) 2.5 1 0 Muscle Physique(EAS) 2 2 0 Your personal trainer suggests that you supplement with as much BCAAs as possible but with no more than 36 grams of creatine and 54 grams of L-glutamine per week. You are thinking of combining Xtend, Gainz, and Strongevity to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications and also includes at least as many servings of Strongevity as Xtend? Xtend servings Gainz servings Strongevity servings How much BCAAs will you obtain?
This exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 5 grams of creatine, 35.5 grams of L-glutamine, and 85 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtend = ___ servings of gainz = ___
MaximizationProblems and Minimization problems ***When using the simplex method, what is the difference between maximizing and minimizing?

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