A company manufactures two products with seasonal demands: We will call them A and B rather than anything clever or imaginative. The monthly demand (1000s) for these two items over the next year is tabled below:

Product	Jan	Feb	March	April	May	June	July	Aug	Sept	Oct	Nov	Dec
A	10	10	10	10	30	30	30	30	30	80	80	80
B	50	50	15	15	15	15	15	15	15	50	50	50

The unit cost of A and B is $5 and $8 respectively when manufactured prior to June. From June to the end of the year the costs fall to $4.50 and $ 7.00 respectively because of the installation of an improved manufacturing system. The combined total of the two products that can be manufactured in any one month cannot exceed 120,000. Further, each unit of A occupies 2 cubic feet and each unit of B, 4 cubic feet of inventory space. Suppose that the maximum inventory space allocated to these items is 150,000 cubic feet and that the holding cost per cubic foot is $0.10/month. Formulate and solve the LP to determine the minimum cost production plan that meets the demand and satisfies the constraints.