Question: For what range of values of h will a sensitive analysis on the effect of a change of h labor-hours be valid

The Cutting Edge Knife Company manufactures paring knives and pocket knives. Each paring knife requires 3 labor-hours, 7 units of steel, and 4 units of wood. Each pocket knife requires 6 labor-hours, 5 units of steel, and 3 units of wood. The profit on each paring knife is $3, and the profit on each pocket knife is $5. Each day the company has available 90 labor-hours, 138 units of steel, and 120 units of wood.

(a) How many of each type of knife should the Cutting Edge Knife Company manufacture daily to maximize its profits?

(b) Suppose that an additional 18 units of steel were available each day. What effect would that have on this optimal solution?

(c) Generalize the search in part (b) to the case where the increase in the number of units of steel available each day is “h” (The value of “”h” can be positive or negative.) For what range of values will result be valid?