QUESTION 1

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 ofloan/investmentAnnual Rate of Return (%)

Automobile loans9

Furniture loans9.5

Mortgage loans5

Other Secured loans9.5

Risk-freesecurities1.5

Fireside will have $2 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 and the Credit Union needs to decide how to allocate the $2 million to each of the loan/investment alternatives to maximize total annual return?

• 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.
• Same amount of funds have to be allocated to automobile and furniture loans.
• 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.

1. Write the linear program equationsfor the loan/investment alternatives listed above?