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