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 10 Other secured loans 11 Signature loans 12. Risk-free securities 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 composition of the loans and investments: Risk-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 signature loans may not exceed the funds invested in risk-free securities. How should the $2 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 the projected total annual return? Annual Retum = $

Answer 1

A В C Max of total Max of total funds Annual Rate of Return (%) Type of Loan/Investment 1 funds available Allocated 2 Automobile loans 3 Furniture loans 4 Other secured loans 5 Signature loans 6 Risk-free securities 8% 10% 11% 12% 10% 9% 30% 7 8 Funds available 2000000 9 10 Type of Loan/Investment 11 Automobile loans 12 Furniture loans 13 Other secured loans 14 Signature loans Allocation 0 0 0 0 15 Risk-free securities 0 16 Total = SUM(B11:B15) 17 18 Total Loans 19 Furniture And other Secured 20 Other secured And signatureSUM(B13:B14) SUM(B11:B14) SUM(B12:B13) 21 22 Return = SUMPRODUCT(B2:B6, B11:B15)

Solver Parameters Set Objective: $B$22 O Min OValue Of: To: 0 Маx By Changing Variable Cells: $B$11:$B$15 Subject to the Constraints: $B$14 < $D$5*$B$18 Add $B$15 $C$6*$B$8 $B$16 < SB$8 Change $B$19 <$B$11 $B$20 <$B$15 Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP 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

A В C Max of total Max of total funds Type of Loan/Investment Annual Rate of Return (%) 1 funds available Allocated 2 Automobile loans 3 Furniture loans 4 Other secured loans 5 Signature loans 6 Risk-free securities 8% 10% 11% 12% 9% 10% 30% 7 8 Funds available 2000000 9 10 Type of Loan/Investment 11 Automobile loans 12 Furniture loans 13 Other secured loans Allocation 630000 170000 460000 14 Signature loans 15 Risk-free securities 16 Total 140000 600000 2000000 17 18 Total Loans 19 Furniture And other Secured 20 Other secured And signature 1400000 630000 600000 21 22 Return 188800 23

Type of Loan/Investment	Allocation
Automobile loans	630000
Furniture loans	170000
Other secured loans	460000
Signature loans	140000
Risk-free securities	600000
Annual Return =	188800