Consider the Pigskin example (c) from Chapter 3. Find Pigskins optimal production policy if, in addition to the given production and holding costs, there is a fixed cost of $50, 000 during any month in which there is positive production. Assume now that storage capacity is 20,000 footballs

(Reference Example 3.3)

The Pigskin Company produces football. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted

monthly demands for the next six months are 10, 000, 15, 000, 30,000, 35,000, 25,000, and 10, 000 Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given month's production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30, 000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month after demand has occurred. The forecasted production costs per football for the next six months are $12.50, $12.55, $12.70, $12.80, $1285, and $12.95 respectively. The holding cost per football held in inventory at the end of any month is figured at 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory. The selling price for football is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occurs-at whatever the selling price is. Therefore, Pigskin wants to determine the production schedule that minimizes the total production and holding costs

Objective To use LP to find the production schedule that meets demand on time and minimizes total production and inventory holding costs(Using Solver)