The employee credit union at State University is planning the allocation of fund
ID: 357952 • Letter: T
Question
The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenueproducing investments together with annual rates of return are as follows:
The credit union will have $2.3 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:
Risk-free securities may not exceed 30% of the total funds available for investment.
Signature loans may not exceed 14% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
Furniture loans plus other secured loans may not exceed the automobile loans.
Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
How should the $2.3 million be allocated to each of the loan/investment alternatives to maximize total annual return?
Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 9 Other secured loans 13 Signature loans 14 Risk-free securities 7Explanation / Answer
Let us assume the following variables which would represent investment in different categories:
Now the problem statement can be defined as:
Max of (0.08A + 0.09B + 0.13C + 0.14D + 0.07E)
Total Investment Opportunity is $2,300,000
Such that:
Risk-free securities may not exceed 30% of the total funds available for investment
Signature loans may not exceed 14% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
D ? 0.14 (A+B+C+D)
Further simplifying the above equation:
Furniture loans plus other secured loans may not exceed the automobile loans.
B+C ? A
Further simplifying the above equation:
Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
C+D ? E
Further simplifying the above equation:
And the last condition is mentioned below:
On solving these 6 equations using the simplex method of linear programming, the investment in each loan vertical is mentioned below, in order to maximize the return:
Maximized Return is $ 216131 which is 9.397% of initial investment of $ 2.3 Million.
Automobile Loans $ 692,300 Furniture Loans $ 227,700 Other Secured Loans $ 464,600 Signature Loans $ 225,400 Risk Free Loans $ 690,000Related Questions
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