GKNTSH produces all wheel driven (AWD) auto differential for sporting utility vehicles (SUV). The demand of AWD is 2000 per month. The production system of GKNTSH can produce this AWD at a rate of 30 units per hour. Setup time to change the settings on the equipment is 2 hours. Worker time (including overhead) is charged at the rate of $50 per hour, and plant idle time during setups is estimated to cost firm $150 per hour in lost profit. GKNTSH has established a 10 percent annual interest charge for determining holding cost. Each AWD differential costs the company $20 to produce; they are sold for $30 per each to customer. Assume 6-hour per day, 20 working days per month, and 12 months per year for your calculation.
a) What is the holding cost per unit AWD differential per year?
b) What is the setup cost?
c) How many AWD differential should GKNTSH produce in each production run to minimize total annual cost?
d) Assuming GKNTSH produces the optimal number (as identified in part c) of AWD differentials in each production run, what is the maximum level of on-hands inventory of AWD differentials that the firm has at any point in time?