Question

Book Calculator Print Item 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 stabilire income. The various revenueproducing investments together with annual rates of return are as follows: Type of Loan/Investment Annual Rate of Return () Automobile loans Furniture loans Other secured loans Signature loans Risk-free securities 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 lan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar Automobile Loans Furniture Loans Other Secured loans 0 Check My Work Previous Next > Al werk saved Email to Save and Exit Submit Assignment for Grading

Answer 1

let

x1 = automobile loans

x2 = furniture loans

x3 = other secured loans

x4 = signature loans

x5 = risk free securities

our objective function is

z = max(0.08x1 + 0.12x2 + 0.14x3 + 0.13x4 + 0.09x5)

constraints

35 < 510,000

24 < 0.10(21 +22+13+14)

-0.10.r1 -0.10.r2 -0.10.r3 + 0.90.04 < 0

T2 + 3 <c1

-r1+12+13 < 0

3 + 4 < 5

→-25 + C3 + 4 <0

x1+x2+x3+x4+x5 = 1,700,000

r1, 22, 23, 24, 25 > 0

Using excel solver we found the optimal solution as

Automobile Loans (x1) = $535,500

Furniture Loans (x2) = $144,500

Other Secured Loans (x3) = $391,000

Signature Loans (x4) = $119,000

Risk Free Loans (x5) = $510,000

Annual Return $176,290 (10.37%)