6 Suppose that the company in Problem 5 owns no labor and raw material but can purchase them at the following prices: as many as 100 hours of skilled labor at $3/hour, 70 hours of unskilled labor at $2/hour, and 30 units of raw material at $1 per unit of raw material. If the company’s goal is to maximize profit, show that the appropriate LP is

a How much should the company pay for an extra unit of raw material?
b How much should the company pay for an extra hour of skilled labor? Unskilled labor? (Be careful here!)

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max z = x + 5x2 s.t. 3x+4x2100 2x1 + 3x2 70 x + 2x2 30 X1, X20 The optimal row 0 for this LP is z + 1.5x + 2.583 + Ma4 = 75 and the optimal solution is z = 75, x = 0, x2 = 15. In an- swering parts (a) and (b), assume that the current basis re- mains optimal.