Question

Tammi’s Truck Stop sells Seat-o-Nails cushions, which are specially designed to keep drivers awake on the road. Her accessories supplier makes deliveries every Tuesday, at which times she can get as many cushions as she wants (the supplier always has extras in his truck). Tammi, who was a statistics major in college, has done some calculations and estimates that weekly demand for cushions is normally distributed with mean 35 and standard deviation 10. The cushions cost her $40 wholesale and she sells them for $75. Tammi uses a 30 percent interest rate to evaluate the cost of holding inventory. It is Tuesday and she has 12 cushions in stock.

The supplier has just arrived. How many cushions should Tammi buy if sales are lost when she runs out of stock during the week?

How many cushions should Tammi buy if a customer who wants a cushion will still buy it when stock has run out, but she has to pay the $5 postage to mail it to the customer?

Answer 1

a) Sales are lost when she comes up short on stock: Underage expense is lost profit:cs= $55-$30 =$25. Overage cost is the expense of holding the pads for one week:co=0.40*3052= $0.2307.Then the base stock is given by:

G(R*) =cscs+co=2525 + 0.2307= 0.9908z0.9908= 2.357R*= 20 + 2.357*12 = 48 So she should purchase 48-12=36 pads.

b)Now, the underage expense is just $4. Thus, we haveG(R*) =cscs+co=44 + 0.2307= 0.9454z0.9454= 1.602R*= 20 + 1.602*12 = 39So she should purchase 39-12=27 pads for this situation, 9 lower than previously.