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October 05, 2015
Math 141 WIR4_Dr. Rosanna Pearlstein 1. 1. Write a system of inequalities whose solution set is the inside of the triangle with vertices (2, −4), (−2, −1) and (4,6). 1
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October 05, 2015
2. Graph each of the following sets of inequalities, and indicate whether the solution set is bounded or unbounded. { 2 − ≥ 4 4 − 2 < −2 { 3 + 4 ≥ 12 2 − ≤ −2 ≤ 3 2
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October 05, 2015
Solve the linear programming problems listed below: Maximize = 10 + 10 subject to { + ≤ 10 3 + ≥ 12 −2 + 3 ≥ 3 ≥ 0, ≥ 0 3
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October 05, 2015
Minimize = 3 + 4 subject to { 30 + 10 ≥ 600 + ≥ 40 3 + 15 ≥ 300 ≥ 0, ≥ 0 4
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October 05, 2015
Agriculture­Crop planning. A farmer plans to plant two crops, A and B. The cost of cultivating Crop A is $40/acre, whereas the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of Crop A requires 20 labor­hours, and each acre of Crop B requires 25 labor­hours. The farmer has a maximum of 3300 labor­hours available. If he expects to make a profit of $150/acre on Crop A, and $200/acre on Crop B, how many acres of each crop should he plant to maximize his profit? 5
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October 05, 2015
Mining. Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $14,000/day to operate, and it yields 50oz of gold and 3000oz of silver each day. The Horseshoe Mine costs $16,000/day to operate, and it yields 75oz of gold and 1000oz of silver each day. Company management has set a target of at least 650oz of gold and 18,000oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost? What is the minimum cost? 6
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October 05, 2015
Madison Finance has a total of $20 million earmarked for homeowner loans and auto loans. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management also has stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns. 7