Problem 9-03 (Algorithmic)
The employee credit union at State University is planning the allocation...

Question

Problem 9-03 (Algorithmic)
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

12

Signature loans

13

Risk-free securities

9

The credit union will have $1.8 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 11% 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 $1.8 million be allocated to each of the loan/investment alternatives to maximize total annual return?

Automobile Loans

$

Furniture Loans

$

Other Secured Loans

$

Signature Loans

$

Risk Free Loans

$

What is the projected total annual return?
$

David · Accepted Answer

SOLUTION:
A= $ Automobile loans
B = $ Furniture loans
C = $ Other secured loans
D = $ Signature loans
E = $ "Risk free" securities
Maximize, annual return: 	0.08A+ 0.10B+ 0.12C+0.13D+0.09E
s.t., 
E 
D 0.11 (A+B+C+D)
B +C A
C+D E
A+B+C+D+E = 1,800,000
After solving,

Problem 9-03 (Algorithmic) 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...

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Type of Loan/Investment	Annual Rate of Return (%)
Automobile loans	8
Furniture loans	10
Other secured loans	12
Signature loans	13
Risk-free securities	9