Given a company orders a product and expects the defective fraction, E(p), to be 5%. Demand is 15,000 units annually and they screen at a rate of 60,000 units annually (think of this as the QC check which is done much quicker than demand arrives). Order cost is $400 per order, holding cost per year is $4 per unit and shortage cost per year is $6 per unit. Unit purchase, screening and disposal costs are $35, $1 and $2, respectively. Selling price of good items is $60 and sell price of imperfect items is $25. The portion of

scrap items in the defective items is 20% (so that the portion of scrap items in lot size y is (0.05)(0.20)(y).

Optimum order quantity is given as y*= sqrt 2kD(h+pie)/h.pie

and optimum maximum backorder allowed is w*=hy*/h+pie

Questions:

a) Calculate the expected total profit per unit.

b) What is the effect of different defective rates on optimal order quantity, backorder quantity and expected total profit per unit? Please display your results graphically as well as a brief description.