# A) Formulate but do not solve the following exercise as a linear programming problem. Madison Finance...

###### Question:

A) Formulate but do not solve the following exercise as a linear programming problem.

Madison Finance has a total of $18 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns P in millions of dollars.  Maximize P = ______ subject to the constraints total loans = ______ distribution of loans = _______ x ≥ 0 y ≥ 0 B) Formulate but do not solve the following exercise as a linear programming problem. A nutritionist at the Medical Center has been asked to prepare a special diet for certain patients. She has decided that the meals are to be prepared from Foods A and B and that the meals should contain a minimum of 420 mg of calcium, 15 mg of iron, and 45 mg of vitamin C. Each ounce of Food A contains 30 mg of calcium, 2 mg of iron, 1 mg of vitamin C, and 2 mg of cholesterol. Each ounce of Food B contains 25 mg of calcium, 0.5 mg of iron, 5 mg of vitamin C, and 5 mg of cholesterol. How many ounces of each type of food should be used in a meal so that the cholesterol content C (in mg) is minimized and the minimum requirements of calcium, iron, and vitamin C are met?  Minimize C = ______ subject to the constraints calcium = _________ iron = ________ vitamin C = __________ x ≥ 0 y ≥ 0 C)Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to$400,000 in two projects. Project A yields a return of 11% on the investment of x dollars, whereas Project B yields a return of 13% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 35% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars?

 Maximize P = ______ subject to the constraints amount available for investment = _________ allocation of funds = __________ x ≥ 0 y ≥ 0

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