Question

Problem 4-03 (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 revenueproducing investments together with annual rates of return are as follows:

Type of Loan/Investment	Annual Rate of Return (%)
Automobile loans	8
Furniture loans	12
Other secured loans	14
Signature loans	13
Risk-free securities	9

The credit union will have $1.6 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 $1.6 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar.

Automobile Loans	$
Furniture Loans	$
Other Secured Loans	$
Signature Loans	$
Risk Free Loans	$

What is the projected total annual return? Round your answer to the nearest dollar.

$  

Answer 1

Let the amount invested in each type be shown as below:

Automobile loans	x1
Furniture loans	x2
Other secured loans	x3
Signature loans	x4
Risk free securities	x5

Total returns = 0.08x1 + 0.12x2 + 0.14x3 + 0.13x4 + 0.09x5. This is the objective function and has to be maximized.

Constraints are:

(1): x1+x2+x3+x4+x5<=$1.6 million or $1,600,000

(2): x5<=30% of $1.6 million or x5<=480,000

(3): x4<=10% of (x1+x2+x3+x4)

(4): x2+x3<=x1

(5): x3+x4<=x5

Lastly there will be a constraint for non-negativity i.e. x1,x2,x3,x4,x5>=0

Solving in excel, using the solver function, the following solution is obtained:

Automobile loans	504,000.00
Furniture loans	136,000.00
Other secured loans	368,000.00
Signature loans	112,000.00
Risk free securities	480,000.00
				Formula
Total return	165,920.00			0.08x1 + 0.12x2 + 0.14x3 + 0.13x4 + 0.09x5
Constraints
1,600,000.00	<=	1,600,000.00		x1+x2+x3+x4+x5<=1,600,000
480,000.00	<=	480,000.00		x5<=480,000
112,000.00	<=	112,000.00		x4<=10% of (x1+x2+x3+x4)
504,000.00	<=	504,000.00		x2+x3<=x1
480,000.00	<=	480,000.00		x3+x4<=x5

How should the $1.6 million be allocated to each of the loan/investment alternatives to maximize total annual return?

	(Amount in $)
Automobile loans	504,000.00
Furniture loans	136,000.00
Other secured loans	368,000.00
Signature loans	112,000.00
Risk free securities	480,000.00

What is the projected total annual return? The total annual return is $165,920

Solver image: