A carpet manufacturer makes four kinds of carpet on a machine. For simplicity, call these four types of carpet, A, B, C, and D. It takes 3 hours to switch production from one type of carpet to another. The demand rates (yards/hr) for the four types of carpet are as follows: 100, 80, 70, and 50. When producing, the machine can produce at the rate of 350 yards/hr. Batch sizes are chosen to minimize inventory while also satisfying the demand requirements. The manufacturer produces with a schedule that cycles through each of the four types, (e.g., A, B, C, D, A, B, . . .).
a. What batch size (yards) is chosen for carpet type A?
b. Suppose they produce 16,800 yards of carpet A in each production cycle (and 50,400 yards of carpet in total within the production cycle). What would be the average inventory of carpet A?