decision.

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

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

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

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$($c$)$ Compare the average profit estimated by simulation in part $($b$)$ to the profit calculation in part $($a$).$

The average profit from the simulation is greater than the profit computed in part $($a$)$

The average profit from the simulation is less than the profit computed in part $($a$).$

Explain why they differ.

Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be higher than the true mean profit.

O Profit is limited by the production quantity, so higher than average demand does not correspond to higher profits, but lower demand will lead to lower profits.

O Profit is limited by the production quantity, so lower than average demand does not correspond to lower profits, but higher demand will lead to higher profits.

O Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be lower than the true mean profit. answers to the nearest integer.$)$

What is the mean profit $($in dollars$)$ associated with $50,000$ units?

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What is the mean profit $($in dollars$)$ associated with $70,000$ units?

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$($e$)$ In addition to mean profit, what other factors should FTC consider in determining a production quantity? $($Select all that apply.$)$

$\backslash (\backslash$square $\backslash )$ probability of a loss

$\backslash (\backslash$square $\backslash )$ probability of a shortage

$-$ gut feeling

$\backslash (\backslash$square $\backslash )$ stock market

profit standard deviation