Answer Happy

Given the linear programming problem below where I i represents the number of belts a company produces and 12 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 2 = 40 +3.22 s.t. 11 + 12 < 40 2.01 +32 < 60 The solution is 11 = I2 = 20 with max 2 = 140. The final tableau is shown below. 1 0 0 21 0 0 1 12 0 1 0 S1 2 2 -1 S2 1 -1 1 rhs Basis 140 2 = 140 20 22 = 20 20 21 = 20 Use this information to answer the following questions. 1. Show that if cı, the coefficient of 71 in the objective function, is between 1 and 5 the current basis remains optimal. 2. Suppose c1 = 5. Find the new maximum z value. 3. Show that if c, 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 tha 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 contribute $5 to profits and would use 2 yards of leather and 2 hours of skilled labor. Should the company manufacture hats?