A company wishes to plan its production of two items with seasonal demands over a six-month period. The demands, in thousands of units, are as follows: Item October 1 2 80 60 November December January 80 80 60 60 20 60 February March 20 60 20 10 The unit production costs of items 1 and 2 are $6 and $10, respectively, provided that they are manufactured prior to January. Starting in January, the unit costs are reduced to $5 and $8 because of the installation of an improved manufacturing system. The total units of items 1 and 2 that can be manufactured during any particular month cannot exceed 140,000. Furthermore, each unit of item 1 occupies 3 cubic feet and each unit of item 2 occupies 6 cubic feet of inventory. The maximum inventory space is 220,000 cubic feet, and the inventory holding cost per cubic foot during any month is $0.15. Formulate a linear programming model to minimize production and inventory costs. Assume that all production takes place at the beginning of the month and, immediately thereafter, demand is met and also that there is no initial inventory..