The Bull Grin Company produces a feed supplement for animal foods produced by a number of other companies. Producing 1,000 pounds of supplement costs $810 on regular time and $900 on overtime. These amounts include materials, which account for more than 80 percent of the cost. The plant can produce 400,000 pounds of supplement per quarter using regular time, but overtime is limited to the production of 40,000 pounds per quarter. The current level of inventory is 40,000 pounds, and management wants to end the year at that level. Holding 1,000 pounds of feed supplement in inventory costs $110 per quarter. Assume hiring and layoff costs are negligible. The latest annual demand forecast follows:

a. Formulate this production-planning problem as a linear program after defining all decision variables.

b. Solve your formulation using a computer package such as POM for Windows.

c. Assume that subcontractors can be hired at $1,100 per thousand pounds to produce as much supplement as Bull Grin requires. Does this change the cost-minimizing solution found in part (b)?

d. If Bull Grin realizes that the current level of inventory is actually 0 pounds, are the resources assumed in part (c) adequate to satisfy all demand and still end the year with 40,000 pounds in ending inventory? If so, how much will the cost of Bull Grin’s production plan increase?

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Quarter 1 2 3 4 Demand (in Pounds) 100,000 410,000 770,000 440,000