7. Consider the situation described in Problem 15 of Section 5.1. (a) Suppose (500+) hr of labor at $18/hr can be used for production, 16 16, with no other change in the data of the problem. Determine the optimal production schedule and profit. (b) Suppose the amount of available raw material M1 is somewhat flexible. With 1 ton available, its marginal value is $7.50/lb. For what interval around 2000lb does M1 retain this marginal value (with all other data as in the original problem)? 5. Combining raw materials M1 and M2 and labor, a company produces units of A,B, and C. The requirements and profit (excluding the cost of labor) for the production and sale of a unit of each are as follows: For the next month, the company has available 1 ton of M1,2.5 tons of M2,500 hr of labor at $18/hr, and up to an additional 120hr of overtime at $24/hr. (The company pays only for the labor used.) To determine an optimal production schedule, the company manager defines x1, x2, and x3 to be the number of A's, B's, and C's to be produced and x4 to be the number of hours of overtime to be used and formulates the following model: Maximizez=105x1+165x2+60x318(2x1+3x2+x3)6x4=69x1+111x2+42x36x4subjectto6x1+12x2+4x316x1+25x2+7x32x1+3x2+x3x420005000500+x4120x1,x2,x3,x40 Adding four slack variables and applying the simplex algorithm, the reduced tableaux resolution (initial and final tableaux only) are shown in Table 5.2