1. A town receives electricity generated from three forms of energy: solar, wind, tide. Consumer demand for electricity based on units of solar, wind, and tide is: Solar: 20 units, Wind: 30 units, Tide: 10 units. Internal Consumption: To convert one unit of solar requires: 0.4 units of solar wind requires: 0.1 units of solar 0.3 units of wind tide requires: 0.3 units of solar 0.2 units of wind 0.1 units of tide 0.2 units of wind 0.1 units of tide 0.5 units of tide S: Amount of solar supplied to meet the demands of the consumer and production (i.e., internal consumption). W: Amount of wind supplied to meet the demands of the consumer and production (i.e., internal consumption). T: Amount of tide supplied to meet the demands of the consumer and production (i.e., internal consumption). Write the three equations that represent the amount of each form of energy supplied to meet the demands of the consumer and production (i.e., internal consumption).

1. A town receives electricity generated from three forms of energy: solar, wind, tide. Consumer demand for electricity based on units of solar, wind, and tide is: Solar: 20 units, Wind: 30 units, Tide: 10 units. Internal Consumption: To convert one unit of solar requires: 0.4 units of solar wind requires: 0.1 units of solar 0.3 units of wind tide requires: 0.3 units of solar 0.2 units of wind 0.1 units of tide 0.2 units of wind 0.1 units of tide 0.5 units of tide S: Amount of solar supplied to meet the demands of the consumer and production (i.e., internal consumption). W: Amount of wind supplied to meet the demands of the consumer and production (i.e., internal consumption). T: Amount of tide supplied to meet the demands of the consumer and production (i.e., internal consumption). Write the three equations that represent the amount of each form of energy supplied to meet the demands of the consumer and production (i.e., internal consumption).

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 84P

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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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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?
2. 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 $5. 8. In Problem 2, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?
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The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($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…
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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].
The Pine Valley Board of Education must hire teachers for the coming school year. The types of teachersand the salaries that must be paid are as follows:Teacher can teach Number applying Annual salaryHistory, science 20 $21, 000History, math 15 $22, 000English, science 12 $23, 000English, math 14 $24, 000English, history 13 $25, 000Science, math 12 $26, 000For example, 20 teachers who are qualified to teach history and science have applied for jobs, and eachof these teachers must be paid an annual salary of $21, 000. Each teacher who is hired teaches the twosubjects he or she is qualified to teach. Pine Valley needs to hire 35 teachers qualified to teach history,30 teachers qualified to teach science, 40 teachers qualified to teach math, and 32 teachers qualified toteach English. The board has $1.4 million to spend on teachers’ salaries. A penalty cost of $1 is incurredfor each dollar the board goes over budget. For each teacher by which Pine Valley’s goals are unmet,the following…
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