IT Computer Services assembles its own brand of personal computers from component parts it purchases overseas and domestically. IT sells most of its computers locally to different departments at State University as well as to individuals and businesses in the immediate geographic region.
IT has enough regular production capacity to produce 160 computers per week. It can produce an additional 50 computers with overtime. The cost of assembly, inspecting, and packaging a computer during regular time is $190. Overtime production of a computer costs $260. Further, it costs $5 per computer per week to hold a computer in inventory for future delivery. IT wants to be able to meet all customer orders with no shortages in order to provide quality service. IT’s order schedule for the next 6 weeks is as follows:
Week Computer orders
1 ..............105
2 ..............170
3 ..............230
4 ..............180
5 ..............150
6 ..............250
IT Computers wants to determine a schedule that will indicate how much regular and overtime production it will need each week in order to meet its orders at the minimum cost. The company wants no inventory left over at the end of the six-week period. Formulate and solve a linear programming model for this problem.