Question

Katie Hammond is paying her way through college by working at various odd jobs. She contracted with the school to produce and sell programs at football games. The cost of producing these is 50 cents each and they sell for $1.25 each. Any not sold at the game are worthless. Demand for programs at each game is normally distributed with a mean of 2,500 and a standard deviation of 200. How many should Katie produce for the upcoming game (round off to the nearest unit)?

Answer 1

Overage cost=incremental cost of unsold item=co=cost-scrap value=0.50-0=$0.50

Underage cost=incremental cost of not meeting the demand=cu=price-cost=1.25-0.50=$0.75

Mean of demand=2500

Standard deviation of demand=200

Let us calculate the value of co/(co+cu)

co/(co+cu)=0.50/(0.75+0.50)=0.40

Suppose we produce Q quantity. So.

Probability of selling (Q+1)th unit should be less than [co/(co+cu)]

or

Let us normalize X,

So,

or

We get z=0.2533

So,

or say 2551