Our bookstore sells mugs for a special event. Unsold mugs are sold after the event for $4.00 each (salvage value). The bookstore's selling price (SP) for the mugs to its customers is $20.00 each. The Bookstore buys the mugs from the supplier at $8.00 each.

Assuming that demand is estimated to be N(545; 112) normally distributed, how many mugs should the bookstore order? It has to place the order much before the event since the mug suppliers has a very long lead time. There's no opportunity to place a second order.

Co = cost of overage (excess stock) = Cost of mug to bookstore minus salvage value

Cs = cost of stocking out = SP of mug minus Cost of mug to bookstore

Cr = Co/(Co + Cs)

P(d>=y) is equal to or greater then the Cr prob figure. (d = demand and y=order qty)

Using the properties of the normal distribution curve, find that optimum order qty (approx.) where profit would be maximized.

Order qty = Avg demand (+ or -) Z x Std Dev.