Consider the product mix problem described in Prob. 3.1-11. Suppose that this manufacturing firm actually encounters price elasticity in selling the three products, so that the profits would be different from those stated in Chap. 3. In particular, suppose that the unit costs for producing products 1, 2, and 3 are $25, $10, and $15, respectively, and that the prices required (in dollars) in order to be able to sell x1, x2, and x3 units are (35 + 100x1–1/3), (15 + 40x2–1/4), and (20 + 50x3–1/2), respectively.
Formulate a nonlinear programming model for the problem of determining how many units of each product the firm should produce to maximize profit.