The demand for ice cream during the six summer months, June, July, August, September, October and November is at all flavors is estimated to be 500, 600, 400, 500, 600 and 400 cartons respectively. Supplier 1 supply all flavors with its ice cream, the price charge changes from month to month according to the following schedule

 

To take advantage of price fluctuation, all favors can purchase more than is needed during a month and store the surplus to help satisfy demand in later month. The cost of refrigerating any ice cream that is left over (surplus) at the end on a month is 5$ per carton. It is now the beginning of June and All-flavors has 10 cartons on-hand. Formulate a linear programming problem to determine a minimum-cost schedule for purchasing ice cream over the next six months from supplier 1, while satisfying demand for ice cream.

Month July August Septembe October November June r Cost($/carton 100$ 110$ 120$ 115$ 108$ 125$