1. What is the new constraint for the finishing resource?

2. The figure shows the graph of the original feasible set for the furniture manufacturing problem drawn with a red boundary. The blue line segments show the change in the feasible set when the new finishing constraint is used. Find the coordinates of points A and B.

3. Determine the optimal solution for the revised linear programming problem. What is the new maximum profit? By how much was the profit increased due to the additional hour for finishing? This amount is the shadow price.
4. Return to the original furniture manufacturing problem, and assume that one additional hour is available for carpentry. Solve the altered problem, and determine the shadow price for the carpentry resource.
5. Use your knowledge of the solution of the original furniture manufacturing problem and the definition of shadow price to explain why the shadow price for upholstery is 0.
6. Fill in the blanks in the following sentence: The shadow price associated with a resource can be interpreted as the change in value of the ______ ______ per unit change of the availability of the resource.

Transcribed Image Text:

y = r + 12 (upholstery) y = -x + 19 (finishing) y = -2x + 32 (carpentry)