24. Powerco has three electric power plants that supply the needs of four cities. Each power plant can supply the following KWH of electricity: Plant 1-500 million; Plant 2- 700 million; Plant 3- 800 million. The peak power demands (in KWH) in the four cities, which occur at the same time (2 p.m.), are as follows: City 1-400 million; City 2-900 million; City 3- 200 million; City 4- 500 million. The cost of sending 1 million KWH from a plant to a city depends on the distance the electricity must travel, and is given in the following table (in $). Solve this problem as a transportation problem. Plant \ City 1 2 3 4 1 12 13 4 4 10 11 10 9. 12 4

24. Powerco has three electric power plants that supply the needs of four cities. Each power plant can supply the following KWH of electricity: Plant 1-500 million; Plant 2- 700 million; Plant 3- 800 million. The peak power demands (in KWH) in the four cities, which occur at the same time (2 p.m.), are as follows: City 1-400 million; City 2-900 million; City 3- 200 million; City 4- 500 million. The cost of sending 1 million KWH from a plant to a city depends on the distance the electricity must travel, and is given in the following table (in $). Solve this problem as a transportation problem. Plant \ City 1 2 3 4 1 12 13 4 4 10 11 10 9. 12 4

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 43P

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1. The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03. Required: a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis. c. What would be the effect on the optimal solution if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?
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1. The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost. REQUIRED: a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.
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A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 780, 900, and 720, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. ProductA ProductB ProductC Dept. I 2 1 2 Dept. II 3 1 2 Dept. II 2 2 1 Profit $18 $12 $15 If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit? product A product B product C What is the maximum profit (in dollars)?
1. The Crumb and Custard Bakery makes coffee cakes and Danish pastries in large pans. The main ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available, and the demand for coffee cakes is 5. Five pounds of flour and 2 pounds of sugar are required to make a pan of coffee cakes, and 5 pounds of flour and 4 pounds of sugar are required to make a pan of Danish. A pan of coffee cakes has a profit of $1, and a pan of Danish has a profit of $5. Determine the number of pans of cakes and Danish to produce each day so that profit will be maximized. REQUIRED: A. Formulate a linear programming model for this problem. B. Solve this model by using graphical analysis. C. How much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?
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The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
A firm is attempting to minimize its shipping costs. The firm has 3 factories and must supply the needs of its 3 customers without shortages. Since the firm has no storage facilities, each factory must make daily shipments to its customers. The table below shows the capacity of each factory, the amount required by each customer, and the cost of shipping from each factory to each customer. Shipping Costs ($/unit) Factory/Capacity Customer 1 Customer 2 Customer 3 A/180 units 13 11 11 B/160 units 7 6 10 C/110 units 5 10 8 Requirement— 225 units Requirement— 75 units Requirement— 150 units Complete the table below to show the quantity shipped from each factory to each customer. (Leave no cells blank - be certain to enter "0" wherever required.) What is the total cost of meeting customer requirements each day?
1 ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops. Instructions: Develop a linear optimization model to determine how many of each type of desk the ABCD company should make next week to maximize profit contribution [Assume: S = units of standard desk produced and D = units of deluxe desk produced. No need to solve the model, neither graphically nor by Solver: just develop the mathematical model for this part].