Jill's Truck Stop sells specialty seat cushions that are designed to keep drivers awake on the road. Her accessories supplier makes deliveries every Tuesday, at which time he can provide her with as many cushions as she needs (he has ample cushions in his truck). Jill has estimated the weekly demand for cushions as normally distributed with mean of 35 and a standard deviation of 10. The cushions cost her $40 wholesale and she sells them for $65. Jill uses a 35% interest rate to evaluate the cost of holding inventory
(a) How many cushions should Jill buy if sales are lost when she runs out of stock during the week? (10%)
(b) How many cushions should she buy if a customer who wants a cushion will still buy it when stock has run out, but Jill will have to pay $5 postage to mail it to the customer? (4%)
(c) How many should she order if she estimates that typically 50% of the sales are lost (as in Part a), and 50% are back ordered (as in Part b)? (4%)