The Cash and Carry Building Supply Company has received the following order for boards in three lengths:

The company has 25-foot standard-length boards in stock. Therefore, the standard-length boards must be cut into the lengths necessary to meet order requirements. Naturally, the company wishes to minimize the number of standard-length boards used. The company must therefore determine how to cut up the 25-foot boards to meet the order requirements and minimize the number of standard-length boards used.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.

c. When a board is cut in a specific pattern, the amount of board left over is referred to as “trim loss.” Reformulate the linear programming model for this problem, assuming that the objective is to minimize trim loss rather than to minimize the total number of boards used, and solve this model. How does this affect the solution?

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Length Order (quantity) 7 ft. 700 9 ft. 1,200 10 ft. 300