West Coast Wood Products Ltd. makes four types of pressed panels from pine and spruce. Each sheet of panel must be cut and pressed. The following table shows hours needed to produce a batch of each type of panel and the hours available each week.

Panel Type   Hours of Cutting        Hours of Pressing

Classic                       1                                    1

Western                    1                                     4

Nouveau                   2                                    3

East Coast                 2                                    2

Available                 80                                 100

There is a limited amount of suitable wood available. The amounts needed for a batch of each type of panel and the maximum weekly availability are given in the following table.

                             Classic western         Nouveau        East        Coast           Availability

Pine                                 50                          40                30            40                   2500

Spruce                            20                          30                50            20                   2000

The profit on each batch of panels is $400 for Classic, $1,100 for Western, $750 for Nouveau and $350 for East Coast. The company wants to maximize profit.

What To Do:

1. Formulate the above production problem as a linear programming program. Then solve it using Excel Solver.

2. Write a memo to the Production Manager summarizing your results. Your memo should clearly address the issues below, using a paragraph for each issue. Be mindful of your grammar, clarity of your statements, and professionalism of your memo because they will be graded.

a. The LP formulation of the problem.

b. The optimal solution including used and unused resources.

c. The range of optimality for the coefficients of the decision variables with a short explanation.

d. The range of feasibility for the resources with a short explanation.

e. Assuming fractional values of the decision variables are not acceptable, solve the problem again as an integer linear program and compare the optimal solution with the one you solved earlier.