In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $30 per doll. During the holiday selling season, FTC will sell the dolls for $38 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.

(a)

Determine the equation for computing FTC's profit for given values of the relevant parameters (e.g., demand, production quantity, etc.).

Using this equation, compute FTC's profit (in dollars) when realized demand is equal to 60,000 (the average demand).

$

(b)

Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of the Dougie doll using a production quantity of 60,000 units.

What is the estimate of the average profit (in dollars) associated with the production quantity of 60,000 dolls? (Use at least 1,000 trials. Round your answer to the nearest integer.)