Question

Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 4% for home loans, 10% for personal loans, and 7% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. (a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max P + Minimum Home Loans Personal Loan Requirement Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Allocation Home Personal Automobile

Answer 1

A)	A	Home Loans - Annual ROR 7%, Must be 40% aka $400,000
	B	Personal Loans- Annual ROR 12%, cannot exceed 60% of auto loans
	C	Auto Loans- Annual ROR 9%
	Max	=	0.07A	+	0.12B	+	0.09C
	$1,000,000	=	A	+	B	+	C
	Constraints:	B	-	0.6C	≤	0
B)	A	=	$400,000
	B	=	$225,000
	C	=	$375,000
	Total Annual Return = $88,750
	Annual % Return = 8.875%
C)	There wouldn't be a change because the the percentages given to the loans are close to identical
D)	There would be an increase of $890.00 because $10,000 was added to the total value
E)	The annual return increases $312.50, which makes a total of $89,062.
	Lastly there was a change from $400,000 because ther ewas a 1% change that must be allocated to home loans