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$\text{'}$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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$($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.

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.

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.

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.

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.

quantities. $($Use at least $1,000$ trials. Round your 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.$)$

stock market

profit standard deviation

gut feeling

probability of a loss

probability of a shortage