Dandy Collectibles is opening a new warehouse. Bob Lee, the warehouse manager, is trying to determine the labor compensation package that most productively utilizes resources. The typical compensation plan offers an hourly wage rate of $13. Mr. Lee is also considering an incentive plan. The incentive plan rewards solely on performance with order pickers earning $0.40/unit prepared for shipping. A typical week shows the number of ordered units that must be prepared for shipping.Errors sometimes happen in Dandy's order picking. Product mishandling occurs in I percent of the orders under the incentive plan and in 0.5 percent of the orders under the hourly wage plan. Errored orders are scrapped and result in lost revenue of $60 per occurrence. Hourly workers pick 20 units per hour. Incentive workers pick 28 units per hour. Regardless of the plan designation,employees work 40-hour weeks. Union restrictions prevent Dandy from operating on Saturday and Sunday. The labor union also restricts Dandy from hiring part-time workers. Orders need not be filled daily, but all orders must be shipped by week’s end (Friday). Assume that hiring and training costs are negligible.
a. How many workers are needed under each plan for the typical week's demand?
b. Which plan meets the typical week’s demand at the lowest cost, including lost sales resulting from errors?