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Homework 4 Additional Problem: Solution 1. Download HW 4 AP.xls from Blackboard. The model and solution are contained on the ﬁrst tab. The optimal solution is to purchase 3718.75 shares of company 2 and 1500 shares of company 4, for a total expected stock value of \$663,750. 2. (a) Z * will increase by at least 25 × 0 = 0 since x 1 = 0 (i.e., it will increase or stay the same). (b) Z * will increase by at least 20 × 3718 . 75 = 74 , 375 since x 2 = 3718 . 75. (c) Z * will decrease by at most 35 × 3718 . 75 = 130 , 156 . 3. (d) Z * will increase by at least 15 × 1500 = 22 , 500 since x 4 = 1500. 3. From Solver’s Sensitivity Report, the dual variables are (1 . 5 , 0 , - 28 . 75). (a) Z * will decrease by at least 50 , 000 × y * 1 = 75 , 000. (b) Z * will increase by at most 100 , 000 × y * 1 = 150 , 000. (c) Z * will decrease by at least 50 , 000 × y * 2 = 0 (i.e., it will decrease or stay the same). (d)

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