Problem: The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year. ECU makes four types of loans and has three additional investment instruments. Each loan/investment has a corresponding risk and liquidity factor (on a scale of 0-1 00, with 100 being the most risky/liquid). The various revenue-producing instruments are summarized in the table below:
|
Instrument
|
Annual Rate of Return (%)
|
Risk Factor
|
Liquidity Factor
|
|
Automobile loans
|
8
|
50
|
0
|
|
Furniture loans
|
10
|
60
|
0
|
|
Other secured loans
|
11
|
70
|
0
|
|
Unsecured loans
|
14
|
80
|
0
|
|
Risk-free securities
|
5
|
0
|
100
|
|
Corporate stock fund
|
9
|
60
|
90
|
|
Corporate bond fund
|
8
|
50
|
80
|
ECU has $2,000,000 available for investment during the coming year. However, state laws and pesky stakeholders impose certain restrictions on choice of investment instruments. Risk-free securities may not exceed 30% of total funds available for investment. Unsecured loans may not exceed 10% of total funds invested in loans. The funds invested in automobile loans must not be less than the total of funds invested in furniture and other secured loans. The average risk factor may not exceed 60, and the average liquidity factor must be at least 40. Formulate a linear program for ECU.