3) Problem 2: Multiperiod Planning Production with overtime production Basel Tool and Die Company (BTD) makes large industrial pipe wrenches in one of its factories. The marketing department estimates demand for this product during the next 6 months to be Month Demand January 370 February 430 March 380 April 450 May 520 June 440 With the current labor force, BTD believes it can make approximately 420 pipe wrenches per month at a cost of $40 per wrench using regular-time production. An additional 80 wrenches per month can be made using overtime production at a cost per wrench of $45. Wrenches can be made in advance and held in inventory for later shipment at a cost of $3 per month per wrench. The monthly demand for wrenches must be satisfied every month. At the end of December (beginning of January) BTD has 10 wrenches in inventory. BTD wants to plan its production, including overtime, and inventory for the next 6 months so as to maximize profit. Assuming the revenue for these wrenches is fixed, the production manager can maximize profit by minimizing the total costs incurred in producing and delivering the wrenches. Note for problem 2. This problem is the same as studied in Lab 7 with overtime production possibilities. In others words, the quantities that the decision maker controls are (1) the number of wrenches to make each month using regular-time production, (2) the number of wrenches to make each month using overtime production, and indirectly (3) the number of wrenches to keep in inventory at the end of each month. We define our decision variables as follows (to keep a clear time convention, we assume that wrenches are made during a month; at the end of the month, wrenches are shipped to customers; any wrench not shipped incurs a holding cost for that month) Rt: number of wrenches made during month t using regular-time production 04: number of wrenches made during month t using overtime production It : number of wrenches in inventory at the end of month t