Smart Home manufactures environmentally efficient ceiling lights to replace those in existing homes. It just received a contract for the next 6 months, requiring 100, 250, 190, 140, 220, and 110 units for each month. Production costs for ceiling lights vary with time due to the specialized materials. Smart Home estimates production will cost $250, $450, $350, $400, $520, and $500 per unit in months 1 through 6, respectively. To take advantage of cost variations, AGW may produce more lights than the contract requires in some months and hold up to 375 of the overproduced in inventory for later months. But holding inventory costs $30 per light per month. Assume there is no beginning inventory. Required:
Formulate a time-phased LP to compute an optimal manufacturing and inventory plan for the next 6 months to minimize total cost.