x1 = $ automobile loans x2 = $ furniture loans x3 = $ other secured loans x4 = $
ID: 373874 • Letter: X
Question
x1 = $ automobile loans
x2 = $ furniture loans
x3 = $ other secured loans
x4 = $ signature loans
x5 = $ "risk free" securities
Max 0.08x1 + 0.10x2 + 0.11x3 + 0.12x4 + 0.09x5
s.t. x5 600,000 [1]
x4 0.10(x1 + x2 + x3 + x4) or -0.10x1 - 0.10x2 - 0.10x3 + 0.90x4 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 = 2,000,000 [5]
x1, x2, x3, x4, x5 0
Objective Function Value =188800.000
Optimal solution:
Automobile Loans (x1) = $630,000
Furniture Loans (x2) = $170,000
Other Secured Loans (x3) = $460,000
Signature Loans (x4) = $140,000
Risk Free Loans (x5) = $600,000
Annual Return $188,800 (9.44%)
Explanation / Answer
The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year. ECU makes four types of loans and has three additional investment instruments. Each loan/investment has a corresponding risk and liquidity factor (on a scale of 0-100, with 100 being the most risky/liquid). The various revenue-producing instruments are summarized in the table below:
Instrument
Annual Rate of Return (%)
Risk Factor
Liquidity Factor
Automobile loans
8
50
0
Furniture loans
10
60
0
Other secured loans
11
70
0
Unsecured loans
14
80
0
Risk-free securities
5
0
100
Corporate stock fund
9
60
90
Corporate bond fund
8
50
80
ECU has $2,000,000 available for investment during the coming year. However, state laws and pesky stakeholders impose certain restrictions on choice of investment instruments. Risk-free securities may not exceed 30% of total funds available for investment. Unsecured loans may not exceed 10% of total funds invested in loans. The funds invested in automobile loans must not be less than the total of funds invested in furniture and other secured loans. The average risk factor may not exceed 60, and the average liquidity factor must be at least 40.
Give the constraints but do not solve and answer the below.
There are seven decision variables ____
There are six constraints (not counting non-negativity).____
We determine the average risk factor by summing risk values and dividing
by 7.____
Risk-free security total investment may exceed $800,000.____
All $2,000,000 must be invested.____
This is a maximization problem.____
This problem cannot be run as an integer program.____
Instrument
Annual Rate of Return (%)
Risk Factor
Liquidity Factor
Automobile loans
8
50
0
Furniture loans
10
60
0
Other secured loans
11
70
0
Unsecured loans
14
80
0
Risk-free securities
5
0
100
Corporate stock fund
9
60
90
Corporate bond fund
8
50
80
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