Reconsider the original version of the Dewright Co. problem summarized in Table 16.8 . After further reflection about the solution obtained by the simplex method, management now is asking some what-if questions.

Table 16.8

(a) Management wonders what would happen if the penalty weights in the rightmost column of Table 1 were to be changed to 7, 4, 1, and 3, respectively. Would you expect the optimal solution to change? Why?

(b) Management is wondering what would happen if the total profit goal were to be increased to wanting at least $140 ­million (without any change in the original penalty weights). Solve the revised model with this change.

(c) Solve the revised model if both changes are made.

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■ Table 16.8 Data for the Dewright Co. nonpreemptive goal programming problem Unit Contribution Product: Penalty Weight Factor 1 2 3 Goal (Units) > 125 (millions of dollars) 5 Long-run profit Employment level Capital investment = 40 (hundreds of employees) < 55 (millions of dollars) 2(+), 4(-) 3 255 15 937 548