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I need help with my QM homework. I don't understand any of it and I am so confused. Please answer all of the questions and provide detailed work with correct answers highlighted or filled in as shown on the document. Thank you!
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Explanation & Answer
hi, I have just completed your assignment, and attached is my solution
PROBLEM 1:
Solution:
We define the variables as follow:
x1 = $ automobile loans
x2 = $ furniture loans
x3 = $ other secured loans
x4 = $ unsecured loans
x5 = $ risk-free securities
x6 = $ cooperate stock funds
x7 = $ cooperate bond funds
The objective of this linear programming model is to maximize the profit
P 8% x1 10% x2 11% x3 14% x4 5% x5 9% x6 8% x7
P 0.08 x1 0.1x2 0.11x3 0.14 x4 0.05 x5 0.09 x6 0.08 x7
Since it is given that ECU has $2,000,000 available for investment during the coming year, the
first constraint can be stated as
x1 x2 x3 x4 x5 x6 x7 2,000,000
Since it is given that risk-free securities may not exceed 40% of total funds available for
investment, the second constraint can be stated as
x5 0.4 x5 x6 x7
0.6x5 0.4 x6 0.4 x7 0
Since it is given that the unsecured loans may not exceed 10% of total funds invested in loans,
the third constraint can be stated as
x4 0.1 x1 x2 x3 x4
0.1x1 0.1x2 0.1x3 0.9 x4 0
Since it is given that the funds invested in automobile loans must not be less than the total of
funds invested in furniture and other secured loans, the fourth constraint can be stated as
x1 x2 x3
x1 x2 x3 0
Since it is given that the average risk factor may not exceed 60, the fifth constraint can be stated
as
avg Risk factor
50 x1 60 x2 70 x3 80 x4 0 x5 60 x6 50 x7
60
x1 x2 x3 x4 x5 x6 x7
50 x1 60 x2 70 x3 80 x4 60 x6 50 x7 60 x1 x2 x3 x4 x5 x6 x7
10 x1 10 x3 20 x4 60 x5 10 x7 0
Since it is given that the average liquidity factor must be at least 40, the sixth constraint can be
stated as
avg Liquidity Factor
0 x1 0 x2 0 x3 0 x4 100 x5 90 x6 80 x7
40
x1 x2 x3 x4 x5 x6 x7
100 x5 90 x6 80 x7 40 x1 x2 x3 x4 x5 x6 x7
40 x1 40 x2 40 x3 40 x4 60 x5 50 x6 40 x7 0
Finally, we have non-negativity constraint, which states that all variables should be greater than
or equal to zero, i.e.
x1 , x2 , x3 , x4 , x5 , x6 , x7 ...