BUSI2013_Unit5Problems.docx - Individual Problem 5 William...

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Individual Problem 5 William Turner BUSI 2013 – Business Decision Analysis Professor: Aniket Mahanti Yorkville University Thursday, May 16 th , 2019
Chapter 8 – 28 (Hints taken from Professor Mahanti) Linear Programming model: Decision variables are the amount invested in the three different investment funds. Let: G = Growth I = Income M = Money Market Max 0.2 G + 0.1 I + 0.06 M s.t. G + I + M \$300,000 G ≥ 30,000 I ≥ 30,000 M ≥ 60,000 0.1G + 0.05I + 0.01M ≤ 15,000 G, I, M ≥ 0 Constraint information Total capital Available G + I + M ≤ \$300,000 Minimum investment in growth fund G/300,000 ≥ 0.1 G ≥ 30,000 Minimum invested in income fund I/300,000 ≥ 0.1 I ≥ 30,000 Minimum invested in money market fund M/300,000 ≥ 0.2 M ≥ 60,000 Max risk profile 0.1G + 0.05I + 0.01M ≤ 0.05 (300,000) 0.1G + 0.05I + 0.01M ≤ 15,000 b) LINGO output for optimal solution on next page. The optimal solution would be to invest \$120,000 in the growth fund, \$30,000 in the income fund, and \$150,000 in the money market fund.
Model Output Sensitivity Analysis c) To determine how the yields on the three funds can vary before the portfolio needs to be modified, we must look at the coefficient ranges.
d) How much of a yield increase can Hartmann expect if the risk index increased to 0.06?
0.06 * 300,000 = 18,000. Changing the risk index to 0.05 changes the R.H. side from 15,000 to 18,000. Since there is an allowable increase of 8100 for this constraint, the shadow price is applicable for this change. The objective value with a risk index of 0.05 = 36,000/300,000 = 0.12 (yield) The objective value with a risk index of 0.06 = 40,668/300,000 = 0.1356 (yield)