Mile-High Microbrewery makes a light beer and a dark beer. Mile-High has a limited supply of barley, limited bottling capacity, and a limited market for light beer. Profits are $0.20 per bottle of light beer and $0.50 per bottle of dark beer.a. The following table shows resource availability of products at the Mile-High Microbrewery. Use the graphic method of linear programming to maximize profits. How many bottles of each product should be produced per month? Product Resource Light Beer(x1) Dark Beer(x2) Resource Availability(per month) Barley Bottling Market 0.1 gram 1 bottle 1 bottle 0.6 gram 1 bottle — 2,000 grams 6,000 grams 4,000 bottles b. Identify any constraints with slack or surplus.

Mile-High Microbrewery makes a light beer and a dark beer. Mile-High has a limited supply of barley, limited bottling capacity, and a limited market for light beer. Profits are $0.20 per bottle of light beer and $0.50 per bottle of dark beer.a. The following table shows resource availability of products at the Mile-High Microbrewery. Use the graphic method of linear programming to maximize profits. How many bottles of each product should be produced per month? Product Resource Light Beer(x1) Dark Beer(x2) Resource Availability(per month) Barley Bottling Market 0.1 gram 1 bottle 1 bottle 0.6 gram 1 bottle — 2,000 grams 6,000 grams 4,000 bottles b. Identify any constraints with slack or surplus.

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...

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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?
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
Tokyo Company needs the resources indicate below to produce its products Product Labor (hr./unit) Material (Ib./unit) Profit (S/unit) $3 2. 2. 3. 4. Tokyo Company has a daily labor capacity of 240 available hours and a daily supply of 400 pounds of material. The general linear programming formulation for this problem is as follows maximize 2 3 + Sxy + 2 subject to Sx + 2 + 4xy s 240 4x + Gry + 3y s 400 Management has developed the following set of goals, arranged in order of their importance to the firm (1) Because of recent labor relations difficulties, management wants to avoid underutilization of normal production capacity (2) Management has established a satisfactory profit level of S500 per day (3) Overtime is to be minimized as much as possible (4) Management wants to minimize the purchase of additional materials to avoid handling and storage problems.
An analyst has started preparing a spreadsheet as shown below. Column A contains the headings for various parameters and Column B contains the analyst's range names to be used in Excel. A B 1 Price per Unit 2 Cost per Unit 3 Profit per Unit PricePerUnit Cost_Per_Unit Profit per Unit 4 5 Fixed Costs Fixed_Costs 6 Variable Costs Variable Costs Label each of the following range names as "Correct" if is a valid range name in Excel or "Incorrect" if the range name is not valid for use in Excel. Proposed Range Name PricePerUnit Cost Per_Unit Profit per Unit Fixed_Costs Variable Costs
Mark has a company that produces tables and chairs, both having two different models. The product models and related information are given in the following table. Wood costs 3000 $ per cubic meter and 200 m3 of wood are available for the upcoming month. The cost of labor is 40 $/hour and there are 6000 hours of labor available in a month. Mark sells his products to a big chain retail company. The company purchases all products whatever Mark produces. Mark formulates an LP as follows to determine the optimal monthly production plan such that he maximizes the total profit. Decision Variables: X1 : number of basic tables to be produced. X2 : number of elegant tables to be produced. X3 : number of basic chairs to be produced. X4 :number of elegant chairs to be produced. Max Z = 140 X1 + 345 X2 + 120 X3 + 260 X4 ( maximize total profit) Subject to 0.11 X1 + 0.13 X2 + 0.06 X3 + 0.07 X4 ≤ 200 (constraint on the available amount of wood) 2 X1 + 4.5 X2 + 1.5 X3 + 4 X4 ≤ 6000…
A linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 1 $0.50 2 $0.70 3 $0.45 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Bean Aroma Rating Taste Rating 75 85 60 85 lb lb lb 450 87 650 74 450 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. (a) What is the minimum-cost blend (in pounds) that will meet the quality standards and provide 1,000 pounds of the blended…
M&L Manufacturing makes various components for printers andcopiers. In addition to supplying these items to a major manufacturer,the company distributes these and similar items to officesupply stores and computer stores as replacement parts forprinters and desktop copiers. In all, the company makes about20 different items. The two markets (the major manufacturerand the replacement market) require somewhat different handling.For example, replacement products must be packagedindividually whereas products are shipped in bulk to the majormanufacturer.The company does not use forecasts for production planning.Instead, the operations manager decides which items to produceand the batch size, based on orders and the amounts in inventory.The products that have the fewest amounts in inventory get thehighest priority. Demand is uneven, and the company has experiencedbeing overstocked on some items and out of others. Beingunderstocked has occasionally created tensions with the managersof…
M&L Manufacturing makes various components for printers andcopiers. In addition to supplying these items to a major manufacturer,the company distributes these and similar items to officesupply stores and computer stores as replacement parts forprinters and desktop copiers. In all, the company makes about20 different items. The two markets (the major manufacturerand the replacement market) require somewhat different handling.For example, replacement products must be packagedindividually whereas products are shipped in bulk to the majormanufacturer.The company does not use forecasts for production planning.Instead, the operations manager decides which items to produceand the batch size, based on orders and the amounts in inventory.The products that have the fewest amounts in inventory get thehighest priority. Demand is uneven, and the company has experiencedbeing overstocked on some items and out of others. Beingunderstocked has occasionally created tensions with the managersof…
What is the nonlinear programming model (OMEGA) used by Texaco?
A linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 1 $0.50 $0.70 2 $0.45 3 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings Indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The Individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Bean Aroma Rating Taste Rating 75 85 60 85 450 87 550 74 350 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. (a) What is the minimum-cost blend (In pounds) that will meet the quality standards and provide 1,000 pounds of the blended coffee…
The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)