use solver to solve, but make sure you formulate and write down that formulation
ID: 3239334 • Letter: U
Question
use solver to solve, but make sure you formulate and write down that formulation before solving.
The U-Save Loan Company is planning its operations for the next year. The company makes four types of loans, listed below, together with the annual return (in percent) to the company.
Legal requirements and company policies place the following limits on the various types of loans.
Signature loans may not exceed 10 percent of the total amount of loans. The amount of signature and furniture loans together may not exceed 20 percent of the total amount of loans. First mortgages must be at least 40 percent of the total mortgages and at least 20 percent of the total amount of loans. The company can lend a maximum of 1.5 million dollars next operating period.
Type Annual Return (percent)
Signature loan 15
Furniture loan 12
Second Home Mortgage 10
First Home Mortgage 7
U-Save wants to know the amounts it should invest in each type of loan to maximize its total annual return.
Explanation / Answer
Ans:X1=Signature loan
X2=Furniture loan
X3=Second Home Mortgage
X4=First Home Mortgage
The optimal solution value is Z = 1.05
X1 = 0
X2 = 0
X3 = 0
X4 = 1.5
0.8 X1 + 0.8 X2 -0.2 X3 -0.2 X4 0
0 X1 + 0 X2 -0.4 X3 + 0.6 X4 0
-0.2 X1 -0.2 X2 -0.2 X3 + 0.8 X4 0
1 X1 + 1 X2 + 1 X3 + 1 X4 1.5 X1, X2, X3, X4 0
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