4. The Buckminster Company produces soccer balls. Buckminster must decide how many soccer balls to produce each month. It has decided to use a six-month planning horizon. The forecasted demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000 respectively. Buckminster wants to meet these demands on time, knowing that it currently has 6000 soccer balls in inventory and it can use a given month's production to help meet demand for that or future months. During each month there is enough production capacity to produce up to 30,000 soccer balls, and there is enough storage capacity to store up to 10,000 soccer balls at the end of the month. The forecasted production costs per soccer balls for the next six months are $15.50, $15.55, $15.70, $15.80, $15.85, and $15.95, respectively. The holding cost per soccer balls held in inventory at the end of any month is figured at 5% of the production cost for that month. (This includes the cost of storage and the cost of money tied up in inventory.) Formulate and solve the math optimization model which will minimize total production and inventory costs in meeting demand for the next six months