Refer to Fig. 6. As the lines of constant profit were lowered, the final line had slope - 8/7 and contained the optimal vertex of the feasible set. Figure 15 shows that, as long as the slope of the final line is between -2 and -1, the optimal solution would still be at the same vertex.

(a) Suppose that the profit per chair is changed from $80 to $ A, but that the profit per sofa remains at $70. Show that the lines of constant profit will each have slope - A/70.
(b) Show that, when - 2 ≤ - A/70 ≤ - 1, then 70 ≤ A ≤ 140. Conclude that the interval [70, 140] is the range of optimality for the profit per chair.
(c) Use similar reasoning to show that the range of optimality for the profit per sofa is [40, 80].

Transcribed Image Text:

m = -1 m = -2 final constant profit line finishing carpentry