Formulate but do not solve the following exercise as a linear programming proble

Question

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

Madison Finance has a total of $20 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 11% 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

Explanation / Answer

Let 'x' million is home loan given and 'y' million auto loan

Maximize P = 0.1x + 0.11y

subject to:

x - 4y 0

x + y 24

Let 'x' million is home loan given and 'y' million auto loan

Maximize P = 0.1x + 0.11y

subject to:

x - 4y 0

x + y 24

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