The employee credit union at State University is planning the allocation of fund

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 revenue-producing investments together with annual rates of return are as follows:

The credit union will have $1.9 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 35% of the total funds available for investment.

• Signature loans may not exceed 12% 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 $1.9 million be allocated to each of the loan/investment alternatives to maximize total annual return?

What is the projected total annual return?

Annual Return = $

Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 9 Other secured loans 10 Signature loans 11 Risk-free securities 9

Explanation / Answer

Total amount available for invesstment = $1.9 million = $1900000

Let

x1 = $ automobile loans

x2 = $ furniture loans

x3 = $ other secured loans

x4 = $ signature loans

x5 = $ "risk free" securities

We have to maximise

0.08x1 + 0.09x2 + 0.10x3 + 0.11x4 + 0.09x5

First condition

x5 < $665,000

Second condition

x4 < 0.12(x1 + x2 + x3 + x4)

= -0.12x1 - 0.12x2 - 0.12x3 + 0.88x4 < 0

third condition

x2 + x3 < x1

=x2 + x3 - x1 < 0

forth condition

x3 + x4 - x5 < 0

fifth condition

x1 + x2 + x3 +x4 + x5 + 1,900,000

x1 , x2 , x3 , x4 , x5 > 0

Solving through simplex Linear progframming

X1 = 543400
X2 = 26600
X3 = 516800
X4 = 148200
X5 = 665000

Annual return = (586872 + 28994 + 568480 + 164502 + 724850) - 1900000

(2073698 - 1900000)/1900000 = 0.09142

i.e annual return is 9.142 %

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