FlexMan, an electronics contract manufacturer, uses its Topeka, Kansas, facility to produce two product categories: routers and switches. Consultation with customers has indicated a demand forecast for each category over the next 12 months (in thousands of units) to be as shown in Table 8-11.

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. Overtime 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 inventory is $3 per month, and the cost of holding a switch in inventory is $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.

a. Assuming no backlogs, no subcontracting, no layoffs, and no new hires, what is the optimum production schedule for FlexMan? What is the annual cost of this schedule? What inventories does the optimal production schedule build? Does this seem reasonable?
b. Is there any value for management to negotiate an increase of allowed overtime per employee per month from 20 hours to 40? What variables are affected by this change?
c. Reconsider parts (a) and (b) if FlexMan starts with only 5,900 employees. Reconsider parts (a) and (b) if FlexMan starts with 6,700 employees. What happens to the value of additional overtime as the workforce size decreases?

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Table 8-11 Demand Forecast for FlexMan