Sydneyville manufactures household and commercial furnishings. The office division produces two desks, rolltop and regular. Sydneyville constructs the desks in its plant outside Medford, Oregon, from a selection of woods. The woods are cut to a uniform thickness of 1 inch. For this reason, one measures the wood in units of square feet. One rolltop desk requires 10 square feet of pine, 4 square feet of cedar, and 15 square feet of maple. One regular desk requires 20 square feet of pine, 16 square feet of cedar, and 10 square feet of maple. The desks yield respectively $115 and $90 profit per sale. At the current time the firm has available 200 square feet of pine, 128 square feet of cedar, and 220 square feet of maple. They have backlogged orders for both desks and would like to produce the number of rolltop and regular desks that would maximize profit. How many of each should they produce?

a. Identify the decision variable.

b. Write down the objective function.

c. Write down the constraints.

d. Find the optimal mix (decision variables) and optimal value (max profit).

e. Sydneyville’s sales manager has renegotiated the contract for regular desks and now expects to make a profit of $125 on each. He excitedly conveys this information to the firm’s production manager, expecting that the optimal mix of rolltop and regular desks will change as a result. Does it?

f. Suppose that the new contract also has higher profit for the rolltop desks. If the new profit for the rolltop desks is $140, how will this change the optimal solution?

g. A logging company has offered to sell Sydneyville an additional 50 square feet of maple for $5.00 per square foot. Based on the original objective function, would you recommend that they accept the offer?

h. Assuming that Sydneyville purchases the 50 square feet of maple, how is the optimal solution affected? i. During inspection, the quality department discovered that 50 square feet of pine had water damage and could not be used. Will it be optimal to produce both desks under these circumstances? Will the product mix change?