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 10 Other secured loans 11 Signature loans 12 Risk-free securities 9 The credit union will have $1.7 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 $1.7 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

• auto: $535,500
• furniture: $144,500
• other secured: $391,000
• signature: $119,000
• risk-free: $510,000
• projected return: $160,480 (9.44%)

Step-by-step explanation:

We can let the variables a, f, o, s, r stand for the amounts invested in auto loans, furniture loans, other secured loans, signature loans, and risk-free securities, respectively. The restrictions imposed are ...

• r ≤ 0.30(1.7·10^6)
• s ≤ 0.10(a +f +o +s)
• f +o ≤ a
• o +s ≤ r
• a +f +o +s +r = 1.7·10^6

And the objective is to maximize ...

p = 0.08a +0.10f +0.11o +0.12s +0.09r

We can write the constraints in standard form as ...

• r -510000 ≤ 0
• -a -f -o +9s ≤ 0
• -a +f +o ≤ 0
• o +s -r ≤ 0
• a +f +o +s +r -1700000 = 0

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It is convenient to formulate this problem as a "solver" problem in a spreadsheet program. The spreadsheet and the solver setup are shown in the attachments. The result is ...

• Automobile Loans $535,500
• Furniture Loans $144,500
• Other Secured Loans $391,000
• Signature Loans $119,000
• Risk Free Securities $510,000

The projected total annual return: $160,480 (9.44%)

_____

Comment on the attachments

The first attachment shows the NeoOffice spreadsheet used to solve this problem. The formula shown is filled in all cells G3:G8. The second attachment shows the Solver setup used to solve this problem. There are actually five constraints. The one not showing is $G$7 = 0.