PlasFib is a manufacturer of synthetic fibers used for making furniture upholstery. It manufactures fiber in 50 colors on one line. When changing over from one color to the next, part of the line must be cleaned, leading to a loss of material. Each changeover costs $120 in lost material and changeover labor. Assume that each changeover requires the line to shut down for 0.5 hour. When it is running, the line produces fiber at the rate of 100 pounds per hour. The fibers sold by PlasFib are divided into three categories. There are five fast-moving colors that average sales of 31,000 pounds per color per year. There are 10 medium-moving colors that average sales of 12,000 pounds per color per year. The remaining are slow-moving products and average sales of 3,200 pounds per year each. Each pound of fiber costs $6 and PlasFib has a holding cost of 15 percent.

a. What is the batch size that PlasFib should produce for each fast-, medium-, and slow-moving color? How many days of demand does this translate into?

b. What is the annual setup and holding cost of the policies you suggested in part (a)?

c. How many hours of plant operation will the above schedule require in a year (including a half-hour of setup per batch)?