Dogie Agency has three police dogs to be assigned to 3 different department stores. The cost of each dog on eachdepartment is given below Dogs SM Robinson CSI 1 200 350 270 2 300 250 150 3 400 350 270 1. What quantitative technique can you utilize for this problem? Explain. 2. Determine the minimum cost of each dog per department.

Dogie Agency has three police dogs to be assigned to 3 different department stores. The cost of each dog on eachdepartment is given below Dogs SM Robinson CSI 1 200 350 270 2 300 250 150 3 400 350 270 1. What quantitative technique can you utilize for this problem? Explain. 2. Determine the minimum cost of each dog per department.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

See similar textbooks

Similar questions

Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?
PRICING SUITS AT SULLIVANS Sullivans is a retailer of upscale mens clothing. Suits cost Sullivans 320. The current price of suits to customers is 350. which leads to annual sales of 300 suits. The elasticity of the demand for mens suits is estimated to be 2.5 and assumed to be constant over the relevant price range. Each purchase of a suit leads to an average of 2.0 shirts and 1.5 ties being sold. Each shirt contributes 25 to profit, and each tie contributes 15 to profit. Determine a profit-maximizing price for suits. In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must determine the prices of shirts and ties, as well the price of suits. Assume that the unit costs of shirts and ties are, respectively, 20 and 15. Continue to assume that, on average, 2.0 shirts and 1.5 ties are sold along with every suit (regardless of the prices of shirts and ties), but that shirts and ties have their own separate demand functions. These demands are for shirts and ties purchased separately from suit purchases. Assume constant elasticity demand functions for shirts and ties with parameters 288,500 and 1.7 (shirts), and 75,460 and 1.6 (ties). Assume the same unit cost and demand function for suits as in Example 7.3. a. How much should the company charge for suits, shirts, and ties to maximize the profit from all three products? b. The assumption that customers will always buy, on average, the same number of shirts and ties per suit purchase, regardless of the prices of shirts and ties, is not very realistic. How might you change this assumption, and change your model from part a accordingly, to make it more realistic?
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
Consider a monopolistically competitive market with NN firms. Each firm's business opportunities are described by the following equations: Demand: Q=100N−PQ=100N−P Marginal Revenue: MR=100N−2QMR=100N−2Q Total Cost: TC=50+Q2TC=50+Q2 Marginal Cost: MC=2QMC=2Q How much profit does each firm make? a: 1,250/N*2−50 b: 2,500/N*2−50 c: 50+625/N*2 d: 1,875/N*2 In the long run, how many firms will exist in this market?
Please note that this question is different from what you have in your library. This question has 3 variables ie 3 departments. Please help solve the problem. A co markets 2 products which are produced in 3 successive departments. The contribution per unit of the 2 products and the production capacity of the 3 departments are X. Y Contribution. 10. 15 Machining dept (hrs) 3. 4 Foundry dept (hrs) 4 2 Painting dept (hrs) 4 5 A constraint on production is that each dept has a limited number of hours available for the forthcoming plan period as shown below: Department. Available hours Machining. 1'200 Foundry. 1000 Painting. 1300 Required- 1. Formulate the linearr programming problem for the above information. 2. Solve them graphically
25. Consider the following list of retail items sold in a small neighborhood gift shop.Average ProfitItem Annual Volume per ItemGreeting cards 3,870 $ 0.40T-shirts 1,550 1.25Men’s jewelry 875 4.50Novelty gifts 2,050 12.25Children’s clothes 575 6.85Chocolate cookies 7,000 0.10Earrings 1,285 3.50Other costume jewelry 1,900 15.00a. Rank the item categories in decreasing order of the annual profit. Classify eachin one of the categories as A, B, or C.b. For what reason might the store proprietor choose to sell the chocolate cookieseven though they might be her least profitable item?
nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 same exampe is used but in this case each plant has a different fixed and variable cost structur and cpacity for manufacturing the differnt Juices. the fixed cost only applies if the plant produces any juice Capacity Unit-Month Fixed…
nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 How much of each juice should be made at each plant in order to minimize total cost while meeting demand and adhering to plant capacity?