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Operatios Research: Linear Programming and Optimization

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1. (20%) A company is planning its aggregate production schedule for the next three months. Units may be produced on regular time or overtime. The relevant costs and capacities are shown in the table below. The demand for each month is also shown. There are two ways of meeting this demand: inventory and current production. Units produced in a particular month may be sold in that month or kept in inventory for sale in a later month. There is a $1 cost per unit for each month an item is held in inventory. Initially, there are 15 units in inventory.

Capacity (units) Production cost
Period Regular time Overtime Regular time Overtime Demand
1 100 20 14 18 60
2 100 10 17 22 80
3 60 20 17 22 140
Formulate an LP model to yield the optimum production plan.