FlexMan, an electronics contract manufacturer, uses its Topeka, Kansas, facility to produce two product categories: routers and switches. Consultation with customers has indi cated a demand forecast for each category over the next $12$ months $($in thousands of units$)$ to be as shown in Table $8-11.1,2001,2001,3001,600$ Manufacturing is primarily an assembly operation, and the number of people on the production line governs capacity. The plant operates $20$ days a month, $8$ hours each day. Production of a router takes $20$ minutes, and production of a switch requires $10$ minutes of worker time. Each worker is paid $$10$ per hour, with a $50$ percent premium for any overtime. The plant currently has $6,300$ employees, Over time is limited to $20$ hours per employee per month. The plant currently maintains $100,000$ routers and $50,000$ switches in inventory. The cost of holding a router in inven tory is $$3$ per month, and the cost of holding a switch in inventory is S$1$ per month. The holding cost arises because products are paid for by the customer at existing market rates when purchased. Thus, if FlexMan produces early and holds in inventory, the company recovers less given the rapidly dropping component prices.