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$)?$

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$($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.

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

The average profit from the simulation is

less than

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.

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 $(40,000$; $50,000$; $60,000$; 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.