Only Fresh Donut Shop" sells donuts to its customers at $0.50 on the day the donuts are made. The demand for fresh doughnuts is normally distributed with a mean of 11000, and a standard deviation of 2000. The leftover day old doughnuts are sold to a secondary market, demand for which is given in the following table which follow a discrete distribution. The price for a day old donut is $0.28. It costs $0.25 to make a doughnut.

Demand Probability

1000 0.15

1200 0.25

1800 0.35

2500 0.25

The goodwill loss for a unit of unmet donut demand is $0.15 for day one .

Using @risk

a. What is the best order quantity (to the nearest 500) to maximize profits? Consider order amounts between 10K and 14K.

b. At the best order quantity from above, what percentage of the time does the company lose money?