Answer:
Maximum returns = $1,980,000
x = Homeowner loans = $17,600,000
y = Auto loans = $4,400,000
Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000
Step-by-step explanation:
From the question we are told that:
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 8% annual rate of return, whereas auto loans yield a 13% annual rate of return.
We have the equation:
Maximum Return = 8% × x + 13% × y
= 0.08x + 0.13y
We are told in the question that
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.
Hence,
x ≥ 4y
So:
x + y = $22,000,000
4y + y = $22,000,000
5y = $22,000,000
y = $22,000,000/5
y = 4,400,000
x = 4y
x = 4(4,400,000)
x = 17,600,000
Maximum Return = 0.08x + 0.13y
= 0.08 × 17,600,000 + 0.13 × 4,400,000
= $1,980,000
Therefore, Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000
