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Formulate but DO NOT solve! Madison Finance has a total of $22 million earmarked

ID: 3005171 • Letter: F

Question

Formulate but DO NOT solve!

Madison Finance has a total of $22 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 9% 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

Explanation / Answer

return from homeowner loans= 0.09x

return from autoloans=0.11y

total return=0.09x+0.11y

maximise 0.09x+0.11y

constraints-

x+y <= 22

x>=4y i.e. x-4y>=0

x>=0

y>=0