A wood-products company produces four types of household furniture. Three basic operations are involved: cutting, sanding, and finishing. The plant’s capacity is such that there is a limit of 900 machine hours for cutting, 800 hours for sanding, and 480 hours for finishing. The firm’s objective is to maximize profits. The initial tableau is as follows: a) What are the shadow prices on each of the constraints? b) What profit for x1 would justify its production? b) What profit for x3 would justify its production? c) If another saw to perform cutting can be rented for $10/hour, should it be procured? What about a finisher at the same price? If either is rented, what will be the gain from the first hour’s use?

Using the simplex algorithm, the final tableau is found to be: Basic variables X2 X4 X7 N Current values 25 140 0 18,000 X1 0 1 2 10 X2 1 X3 18 32 HN " 130 X4 1 X6 3/12 - 1/16 X5 SE 16 56 LE I 12 - 15 X7 1