Bellows Lumber Yard, Inc. stocks standard length, 25-foot boards, which it cuts to custom lengths to fill individual customer orders. An order has just come in for 5,000 7-foot boards,1,200 9-foot boards, and 300 11-foot boards. The lumber yard manager has identified six ways to cut the 25-foot boards to fill this order. The six cutting patterns are summarized in the following table.

One possibility (cutting pattern 1) is to cut a 25-foot board into three 7-foot boards, and not to cut any 9- or 11-foot boards. Note that cutting pattern 1 uses a total of 21 feet of board and leaves a 4-foot piece of scrap. Another possibility (cutting pattern 4) is to cut a 25-foot board into one 7-foot board and two 9-foot boards (using all 25 feet of the board). The remaining cutting patterns have similar interpretations. The lumber yard manager wants to fill this order using the fewest number of 25-foot boards as possible. To do this, the manager need to determine how many 25-foot boards to run through each cutting pattern.

a. Formulate an LP model for this problem.

b. Create a spreadsheet model for this problem and solve it using Solver.

c. What is the optimal solution?

d. Suppose the manager wants to minimize waste. Would the solution change?"

Number of Boards Produced \begin{tabular}{cccc} \hline Cutting Pattern & 7ft & 9ft & 11ft \\ \hline 1 & 3 & 0 & 0 \\ 2 & 2 & 1 & 0 \\ 3 & 2 & 0 & 1 \\ 4 & 1 & 2 & 0 \\ 5 & 0 & 1 & 1 \\ 6 & 0 & 0 & 2 \end{tabular}