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: 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

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?

Type of Loan/Investment	Fund Allocation
Automobile loans	$
Furniture loans	$
Other secured loans	$
Signature loans	$
Risk-free securities	$

What is the projected total annual return?

Answer 1

Max of total funds available Max of total funds Allocated Type of Loan/Investment 2 Automobile loans 3 Furniture loans 4. Other secured loans 5 Signature loans 6 Risk-free securities Annual Rate of Return (%) 8% 9% 10% 11% 9% 12% 35% 7 8 Funds available 1900000 9 10 Type of Loan/Investment Allocation | 11 Automobile loans 12 Furniture loans 13 Other secured loans 14 Signature loans 0 15 Risk-free securities 16 Total = SUM(B11:B15) 17 18 Total Loans = SUM(B11:B14) 19 Furniture And other Secured = SUM(B12:B13) 20 Other secured And signature = SUM(B13:B14) 21 22 Return = =SUMPRODUCT(B2:B6, B11:B15) 0 23

Solver Parameters Set Objective: $B$22 To: O Max O Min O Value of: By Changing Variable Cells: $B$11:$B$15 Add Subject to the Constraints: $B$14 <= $D$5*$B$18 $B$15 <= $C$6*$B$8 $B$16 <= $B$8 $B$19 <= $B$11 $B$20 <= $B$15 Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative Select a Solving Simplex LP Method: Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Α Annual Rate of Return (%) Max of total funds available Max of total funds Allocated 1 Type of Loan/Investment 2 Automobile loans 3 Furniture loans 4. Other secured loans 5 Signature loans 6 Risk-free securities 7 8 Funds available 8% 9% 10% 11% 9% 12% 35% 1900000 9 Allocation 10 Type of Loan/Investment 11 Automobile loans 12 Furniture loans 13 Other secured loans 14 Signature loans 15 Risk-free securities 16 Total 17 18 Total Loans 19 Furniture And other Secured 20 Other secured And signature 21 22 Return = 543400 26600 516800 148200 665000 1900000 1235000 543400 665000 173698

Type of Loan/Investment	Allocation
Automobile loans	543400
Furniture loans	26600
Other secured loans	516800
Signature loans	148200
Risk-free securities	665000
Annual Return =	173698