1 Glassco manufactures glasses: wine, beer, champagne, and whiskey. Each type of glass requires time in the molding shop, time in the packaging shop, and a certain amount of glass. The resources required to make each type of glass are given in Table 32. Currently, 600 minutes of molding time, 400 minutes of packaging time, and 500 oz of glass are available. Assuming that Glassco wants to maximize revenue, the following LP should be solved:

a Find the dual of the Glassco problem.
b Using the given optimal primal solution and the Theorem of Complementary Slackness, find the optimal solution to the dual of the Glassco problem.
c Find an example of each of the complementary slackness conditions, (40)–(43). As in the text, interpret each example in terms of shadow prices.

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max z= 6x1 +10x+9x3 + 20x4 s.t. 4x1 + 9x2 + 7x3 + 10x4600 (Molding constraint) x1 + x2 + 3x3 + 40x4 400 (Packaging constraint) 3x1 + 4x2 + 2x3 + X4 500 (Glass constraint) X1, X2, X3, X4 0 2800 3 It can be shown that the optimal solution to this LP is z = x=400, x = 0, x = 0, x = 0, s = 0, $2 = 0, 53 420, x3 = 280. 3