Question 4 (20 points): The employee credit union at State University is plannin

Question

Question 4 (20 points): 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: Annual Rate of Return (%) Type of Loan/Investment Automobile louns Furniture loans Other secured loans Signature loans Risk-free securities 10 The credit union will have $2 million available for investment during the coming year. State laws and credit union policies inpose 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, fiuniture, 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. Formulate the linear programming problem for maximization issue.

Explanation / Answer

Autombile be x, Furniture be y, Other Secured be z, Signature be a, Risk free be b

Max. 8%*x+10%*y+11%*z+12%*a+9%*b

s.t.

b<=30%*(x+y+z+a+b) or b<=30%*2000000

x+y+z+a+b<=2000000

a<=10%*(x+y+z+a)

y+z<=x

z+a<=b

x,y,z,a,b>=0

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