MACHINE PRODUCTION PLANNING Problem A company produces two products A and B using two machines X and Y. The company needs to plan the production over three months. Each product can be produced in any of the machines. The machine-hours required for production, the production capacity (in hours) and the estimated product demand are given in the tables. The cost for using one machine hour is $30 and the cost of inventory-holding one unit of each product per month is $10. For example, producing 60 units of product A in machine A and none in machine B, during month 1, has a cost of $3600. Since only 50 units are needed in month 1, the extra 10 units can be hold in inventory for month 2 at a cost of $100. The company wants to decide the production plan in order to meet exactly the estimated demand in each month at the minimum overall cost of machine-hours and inventory-holding. Hours on machine X Hours on machine Y Product A Product B 2.0 2.5 1.5 2.0 Month 1 2 3 Capacity Capacity machine X machine Y 140 250 60 150 80 100 Demand Demand product A product B 50 30 100 50 60 50