Answer Happy

Given the linear programming problem below where 1, represents the number of belts a company produces and represents the number of pairs of gloves produced. The first constraint is for the number of square yards leather available and the second for the number of hours of skilled labor available. Max := 4 + 379 st. 11+39 340 21, + 12 560 The solution is r1 12 = 20 with max : = 140. The final tableau is shown below. 11 81 1 0 0 2 1 140 = = 140 0 0 1 2 - 1 20 g = 20 010-11 2 = 20 Use this information to answer the following questions. 1. Show that if the coefficient of in the objective function is between 1 and the current basis remains optimal 82 rhs Basis 20 2. Suppose q = 5. Find the new maximum = value. 3. Show that if oz is between 2 and 4 the current basis remains optimal. 4. Show that if the available leather is between 30 and 60 yards the current basis remains optimal. 5. Show that if the number of hours of skilled labor is between 40 and 80 the current basis remains optimal 6. The company is considering manufacturing leather hats. Each hat would contributes to profits and would use 2 yards of leather and 2 hours of skilled labor. Should the company manufacture hats?