The supplier of a product wants to discourage large quantity purchases. Suppose that all the assumptions of the basic EOQ apply except that a reverse quantity discount is applicable; that is, the unit variable cost is given by v =  v0 0 ≤ Q < Qb v0(1 +

d) Qb ≤ Q

a. Write an expression (or expressions) for the total relevant costs per year as a function of the order quantity Q. Introduce (and define) whatever other symbols you feel are necessary.

b. Using graphical sketches, indicate the possible positions of the best order quantity (as is done in Figure 4.5 for the regular discount case).

c. What is the best order quantity for an item with the following characteristics:

Demand rate = 50,000 units/year Fixed setup cost per replenishment = $10 v = $1.00/unit d = 0.005 Selling price = $1.44/unit Carrying charge = 0.20 $/$/year Qb = 1,500 units