Sanders Fishing Supply of Naples, Florida, manufactures a variety of fishing equipment that it sells throughout the United States. For the next three months, Sanders estimates demand for a particular product at 150, 250, and 300 units, respectively. Sanders can supply this demand by producing on regular time or overtime. Because of other commitments and anticipated cost increases in month 3, the production capacities in units and the production costs per unit are as follows:

Inventory may be carried from one month to the next, but the cost is $20 per unit per month. For example, regular production from month 1 used to meet demand in month 2 would cost Sanders $50 + $20 = $70 per unit. This same month 1 production used to meet demand in month 3 would cost Sanders $50 + 2($20) = $90 per unit.
a. Develop a network representation of this production scheduling problem as a transportation problem.
b. Develop a linear programming model that can be used to schedule regular and overtime production for each of the three months.
c. What is the production schedule, how many units are carried in inventory each month, and what is the total cost?
d. Is there any unused production capacity? If so,where?

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Production Capacity (units) 275 100 200 50 100 50 Cost per Unit Month 1-Regular Month 1-Overtime Month 2-Regular Month 2 Overtime Month 3-Regular Month 3-Overtime $ 50 80 50 80 60 100