The employee credit union at State University is planning the allocation of fund
ID: 328176 • Letter: T
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 varlous revenue-producing 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 $1.9 million available for Investment during the coming year. State laws and credit union policles impose the following restrictions on the composition of the loans and investments: 9 10 Risk-free securities may not exceed 35% of the total funds available for investment. * Signature loans may not exceed 12% 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 $1.9 million be allocated to each of the loan/investment alternatives to maximize total annual return? Type of Loan/Investment Automobile loans Furniture loans Other secured loans Signature loans Risk-free securities What is the projected total annual return? Annual Return Fund AllocationExplanation / Answer
Lets define variables:
x1 = $ automobile loans
x2 = $ furniture loans
x3 = $ other secured loans
x4 = $ signature loans
x5 = $ "risk free" securities
Objective value:
MAX 0.08x1 + 0.09x2 + 0.10x3 + 0.11x4 + 0.09x5
s.t. x5 less than or equal to 0.35 (1.9 million) = x5 less than or equal to $6,65,000
x5 ? 665,000 [1]
x4 ess than or equal to 0.12(x1+x2+x3+x4)=0.90x4-0.12x1-0.12x2-0.12x3 less than or equal to 0
x4 ? 0.12(x1 + x2 + x3 + x4) or
-0.12x1 - 0.12x2 - 0.12x3 + 0.88x4 ? 0 [2]
x2 + x3 ? x1 or
- x1 + x2 + x3 ? 0 [3]
x3 + x4 ? x5 or
+ x3 + x4 - x5 ? 0 [4]
x1 + x2 + x3 + x4 + x5 = 1,900,000 [5]
x1, x2, x3, x4, x5 ? 0
After solving these equations through online linear programming calculator (Simplex method), I got these values-
Optimal solution:
Automobile Loans (x1) = $543,400
Furniture Loans (x2) = $26,600
Other Secured Loans (x3) = $516,800
Signature Loans (x4) = $148,200
Risk Free Loans (x5) = $665,000
Annual Return $173,698
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