A racing bike manufacturer called MBX is using a special pillion seat in its brand new bike model. Sales for this model show a fairly steady demand of 5,600 bikes per year. Traditionally, MBX purchases these seats from a producer in Germany at a price of $8/unit. It costs MBX $100 to place an order. Inventory holding costs are based on an annual interest rate of 20%. Suppose that the seat supplier is offering a quantity discount applied to all units with the following schedule (c is the per-unit purchasing cost and Q is the ordering quantity):
c = $8/unit if Q ≤ 700
$7/unit if 700
$6/unit if 900≤Q
a) Determine the optimal order quantity of each of the three quantity intervals.
b) Determine the minimal total cost (sum of setup, inventory holding, and purchase cost) for each interval, and determine the optimal order quantity for this problem.