Question

The Fireside Credit Union 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:

Type of loan/investment    Annual Rate of Return (%)

Automobile loans 5 Furniture loans    15

Mortgage loans 6 Other Secured loans    12

Risk-free securities 2

Fireside will have $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.

• Automobile, furniture and other secured loans may not exceed the amount invested in Mortgage loans

• Furniture and automobile loans together may not exceed the amount invested in risk-free securities

• Other Secured loans may not exceed 10% of the funds invested in all other types of loans (automobile, furniture, and mortgage).

• Risk-free securities may not exceed 15% of the total funds available for investment.

How should the $3 million be allocated to each of the loan/investment alternatives to maximize total annual return? What is the projected total annual return? Write a linear program and use Excel Solver to find the solution.

Answer 1

Let x1,x2,x3,x4,x5 are the investments in loans types Automobile , Furniture ,Mortgage loans, Other Secured loans, and risk free securities loans as listed above.

Total return = Maximize (0.05X1 + 0.15X2 + 0.06X3 + 0.12X4 + 0.02X5)

Subject to constraints:

X1, X2, X3, X4, X5 >= 0

And, X1+X2+X3+X4+X5 <= 3,000,000

X5 <= 450,000

X1 + X2 +X4 <= X3

X2 + X1 <= X5

X4 <= 0.10 (X1+X2+X3)

Using Solver:

Formulae:

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