Green Thumb, a manufacturer of lawn care equipment, has introduced a new model of lawnmower.Each unit costs $250 to manufacture, and the introductory price is $450.At this price, the anticipated demand is normally distributed, with a mean of = 5000 and a standard deviation of = 3000.Any unsold units at the end of the season will be disposed of in a post-season sale for $200 each.

1. How many units should Green Thumb manufacture for sale?
2. What is the expected profit from this policy?
3. How many customers does Green Thumb expect to turn away because of stocking out?

Newsvendor Formulas

CR = C_u / [C_u + C_o]

Q = + z

Excel formula for z: = NORMSINV(CR)

Once Q and z are known:

Expected Lost Sales (i.e. understock): ELS = X Loss(z)

To find Loss(z), you can use the Standard Normal Loss table, or

In Excel: Loss(z): = NORMDIST(z,0,1,0) - z*(1-NORMSDIST(z))

Expected Sales: ES = - ELS

Expected Leftover Inventory (i.e. overstock): ELI = Q - ES

Expected Profit: EP = C_u X ES - C_o X ELI