1.)Appalachian Designs is a small manufacturer of furniture items that are sold throughout the summer at local festivals. Their production manager, J. P. Weaver, has to determine how many of each product to manufacture during the Spring production period. The products will require time on a planer, time on a lathe, and time in a finishing division. The time required for each product, the profit per unit, the maximum allowable production, the minimum production batch lot for each product, and the total hours available, are listed in the following table:

Profit PerMaximumMinimum

ProductsPlanerLatheFinishingUnitProductionBatch Size

A.3.05.15$7.20700100*

B.2.03.08$5.801000200

C.5.12.28$11.1030075

D.3.07.18$8.40600150

E.4.10.22$9.30500100

Hours Avail30080200

*This means that for Product A, they may produce none at all, but if they produce, they must produce between 100 and 700 units. The same is true of all products.

Mr. Weaver would like to maximize profits, given the resources available. You are to provide the linear program that will assist him in these decisions.