$($All answers were generated using $1,000$ trials and native Excel functionality.$)$

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 $$34$ per doll. During the holiday selling season, FTC will sell the dolls for $$40$ 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 uncertain. The normal probability distribution with an average of $60,000$ dolls and a standard

deviation of $15,000$ 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$)$ Create a what$-$if spreadsheet model using formulas that relate the values of production quantity, demand, sales, revenue from sales,

amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit when demand is equal to its average

$(60,000$ units$)?$

$

$($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 associated with the production

quantity of $60,000$ dolls? Round your answer to the nearest dollar.

$

How does this compare to the profit corresponding to the average demand $($as computed in part $($a$))?$

The average profit from the simulation is

the profit computed in part $($a$).$

$($c$)$ Before making a final decision on the production quantity, management wants an analysis of a more aggressive $70,000-$unit production

quantity and a more conservative $50,000-$unit production quantity. Run your simulation with these two production quantities. What is the

average profit associated with each? Round your answers to the nearest dollar. If your answer is negative, use a minus sign.

When ordering $50,000$ units, the average profit is approximately $

When ordering $70,000$ units, the average profit is approximately $

$($d$)$ Besides average profit, what other factors should FTC consider in determining a production quantity? Compare the four production

quantities ; and $70,000)$ using all these factors.

If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. Round the other

answers to the nearest dollar. If your answer is negative, use a minus sign. $($c$)$ Before making a final decision on the production quantity, management wants an analysis of a more aggressive $70,000-$unit production quantity and a more

conservative $50,000-$unit production quantity. Run your simulation with these two production quantities. What is the average profit associated with each? Round

your answers to the nearest dollar.

When ordering $50,000$ units, the average profit is approximately $

When ordering $70,000$ units, the average profit is approximately $

$($d$)$ Besides average profit, what other factors should FTC consider in determining a production quantity? Compare the four production quantities ;

$60,000$ ; and $70,000)$ using all these factors.

If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. Round the other answers to the nearest dollar.