Northwest Pipe (NP) makes water pipe. NP is planning production for the next seven months,March through September. The forecast demands (in thousands of feet) are, respectively, 40, 60, 70, 80, 90, 100, and 80. NP can make 75,000 feet of pipe per month using regular-time production, at a cost of $1.25 per foot. They can make up to an additional 15,000 feet using overtime production at a cost of $1.50 per foot. Any pipe made in one month and sold in a later month incurs an inventory holding cost of $0.15 per foot, per month. NP expects to end February with 5000 feet of pipe and would like to plan to end September with 10,000 feet in inventory. NP would like to plan their production schedule to minimize total cost during the next seven months.

(a) Formulate an LP to minimize total costs.
(b) Set up and solve the problem on a spreadsheet.
(c) What is the optimal solution? Explain the rationale for the solution.