Problem 4-03 (Algorithmic) The employee credit union at State University is plan
ID: 431336 • Letter: P
Question
Problem 4-03 (Algorithmic)
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 10% 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? Round your answers to the nearest dollar.
What is the projected total annual return? Round your answer to the nearest dollar.
$
Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 12 Other secured loans 14 Signature loans 13 Risk-free securities 9Explanation / Answer
Max 0.08x1+0.12x2+0.14x3+0.13x4+0.09x5
Constraints=
x5<=690,000 (1)
x4<=0.10(x1+x2+x3+x4) or -.10x1-.10x2-.10x3+.90x4<=0 (2)
x2+x3<=x1 or –x1+x2+x3<=0 (3)
x3+x4<=x5 or +x3+x4-x5<=0 (4)
x1+x2+x3+x4+x5=2,300,000 (5)
x1,x2,x3,x4,x5>0
Projected Total Annual return = 0.08(724500)+0.12(195500)+0.14(529000)+0.13(161000)+0.09(690000)
=57960+23460+74060+20930+62100=$238,510
=10.37%
Automobile Loans
$ 724,500
Furniture Loans
$ 195,500
Other Secured Loans
$ 529,000
Signature Loans
$ 161,000
Risk Free Loans
$ 690,000
Automobile Loans
$ 724,500
Furniture Loans
$ 195,500
Other Secured Loans
$ 529,000
Signature Loans
$ 161,000
Risk Free Loans
$ 690,000
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