Rapallo Corporation manufactures industrial vacuum cleaners with forecasted sales for the next five weeks as follows: Week 1 = 2,000 units, Week 2 = 2,500, Week 3 = 3,000, Week 4 = 3,000, and Week 5 = 3,500. Beginning inventory equals 13,000 units and the firm wants to maintain this level at the end of week 5. 

a. What weekly production rate is necessary?

b. What is the ending inventory level over time using your answer in part a?

c. Suppose management wants to reduce its inventory level to 3,000 units by the end of week 5 because the chief financial officer is upset about the cost to carry so much inventory. How does the production plan and rate change?