2. Madison, Inc. stocks Part# OTM700. The annual demand rate for the part is constant and known to be 4000 units/year. The part is purchased at a cost of $4/unit from an independent supplier. The annual holding cost for Part# OTM700 is 25% of the per-unit purchase price, per year. Every time an order is placed, a fixed cost of $80 is incurred. a) What is the optimal order quantity for minimizing the average annual total cost? What is the optimal number of times per year for Madison, Inc. to place an order? What is the corresponding average annual total cost? b) Suppose there is a new supplier that charges only $3.90 per unit, but this supplier requires that the order quantity be x units or more. The fixed cost of ordering and the annual inventory carrying cost remain at $80/order and 25% of the per-unit purchase cost, respectively. For what range of values of x will Madison, Inc. choose the new supplier over the current supplier? (For example, if x = 10, which supplier would Madison, Inc. prefer? What if x = 1000? 2000? Etc.)