Chapter 3.4, Problem 17E

PRODUCTION SCHEDULING Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $2. and the profit for each model B grate is $1.50. 1000 lb of cast iron and 20 labor-hours are available for the production of grates each day. Because of an excess inventory of model B grates, management has decided to limit the production of model B grates to no more than 200 grates per day. How many grates of each model should the division produce daily to maximize Kane's profit?

a. Use the method of corners to solve the problem.

b. Find the range of values that the contribution to the profit of a model A grate can assume without changing the optimal solution.

c. Find the range of values that the resource for cast iron can assume without changing the optimal solution.

d. Find the shadow price for the resource for cast iron.

e. Identify the binding and nonbinding constraints.