Consider the carload discount schedule pictured in Figure 4–13 (page 225). Suppose M  500 units, C  $10 per unit, and a full carload of 500 units costs $3,000.

a. Develop a graph of the average cost per unit, C(Q)Q, assuming this schedule.

b. Suppose that the units are consumed at a rate of 800 per week, order setup cost is

$2,500, and holding costs are based on an annual interest charge of 22 percent.

Graph the function G(Q)  C(Q)Q  KQ  I(C(Q)Q)Q2 and find the optimal value of Q. (Assume that 1 year  50 weeks.)

c. Repeat part

(b) for   1,000 per week and K  $1,500.