# Optimization: optimization – #77

Question: Each year, a shoe company faces demands (which must be met on time) for pairs of shoes as shown below:

Quarter1 Demand: 6000

Quarter2 Demand: 3000

Quarter3 Demand: 8000

Quarter4 Demand: 1000

Workers work three consecutive quarters and then receive one quarter off. For example, a worker might work during quarters 3 and 4 of one year and quarter 1 of the next year. During a quarter in which a worker works, he or she can produce up to 500 pairs of shoes. Each worker is paid $5000 per quarter. At the end of each quarter, a holding cost of$10 per pair of shoes is assessed. Determine how to minimize the cost per year (labor plus holding) of meeting the demands for shoes. To simplify matters, assume that at the end of each year, the ending inventory is zero. (Hint: you may assume that a given worker will get the same quarter off during each year.)