The employess credit union at State University is planning the allocation of fun

Question

The employess 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 inversts in risk-free securities to stablize 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                                                            8

Furniture loans                                                               10

Other secured loans                                                       11

Signature loans                                                               12

Rosk-free securities                                                         9

The credit union will have $2 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the coming position of the loans and investments:

* Rish-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 sugnature loans may not exceed the funds invested in risk-free securities.

Suppose the following changes have occurred:

The total amount available for investment is $1 million.

An additional constraint is: auto loans plus furniture loans must not exceed 30% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).

Write down the correspongding TWO constraints. Use variable names:

A = $ automobile loans

F = $ furniture loans

O = $ other secured loans

s = $ signature loans

R = $ "rish free" securities

Explanation / Answer

Assuming that credit union will maximize the returns on its investment we have a maximization quotient as Z

Z = 8% A + 10% F + 11% O + 12% S + 9% R

Constraints before the changes are:

1 A +F + O + S + R <= $ 2,000,000

2 R <= $ 600,000

3 S <= 10% (A + F+O+S)

4 F + O <= A

5 O + S <= R

Constraints after the changes:

1 A + F + O +S +R <= $ 1,000,000

2 R <= $ 300,000

3 S <= 10% (A + F+O+S)

4 F + O <= A

5 O + S <= R

6 A + F <= 30% (A + F + O + S)

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