Formulate but do not solve the following exercise as a linear programming problem. Madison Finance has a total of $15 million earmarked for homeowner and auto loans. 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 in dollars of homeowner loans should be greater than or equal to nine times the total amount in dollars of automobile loans. Determine the total amount of loans of each type Madison should extend to each category in order to maximize its returns.
A) Maximize: Subject to:
B) Maximize: Subject to:
C) Maximize: Subject to:
D) Maximize: Subject to:

Question

Formulate but do not solve the following exercise as a linear programming problem. Madison Finance has a total of $15 million earmarked for homeowner and auto loans. 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 in dollars of homeowner loans should be greater than or equal to nine times the total amount in dollars of automobile loans. Determine the total amount of loans of each type Madison should extend to each category in order to maximize its returns.
A) Maximize: Subject to: 
B) Maximize: Subject to: 
C) Maximize: Subject to: 
D) Maximize: Subject to:

Quizplus · Accepted Answer

Let x be the total amount of homeowner loans and y be the total amount of auto loans.
The objective is to maximize the total return, which is 0.10x + 0.11y.
The constraint is that x + y = 15 (total amount of loans), and x ≥ 9y (requirement of homeowner loans being greater than or equal to nine times auto loans).
Therefore, the problem can be formulated as:
Maximize: 0.10x + 0.11y
Subject to: x + y = 15
              x ≥ 9y
This can be further simplified to:
Maximize: 10x + 11y
Subject to: x - 9y ≥ 0
              x + y = 15
where the coefficients are multiplied by 100 for convenience. This is equivalent to option B.

Formulate but Do Not Solve the Following Exercise as a Linear