Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production lien. The plant operates 20 days a month, eight 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 $2 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.

Demand For FlexMan
Month	Router Demand	Switch Demand
January	1,800	1,600
February	1,600	1,400
March	2,600	1,500
April	2,500	2,000
May	800	1,500
June	1,800	900
July	1,200	700
August	1,400	800
September	2,500	1,400
October	2,800	1,700
November	1,000	800
December	1,000	900

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?