Model File Available: 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$).$

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

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

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

Explain why they differ.

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.

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 lower than average demand does not correspond to lower profits, but higher demand will lead to higher profits. Run your simulation with these two production 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? $($d$)$ 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. $($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.$)$

profit standard deviation

probability of a shortage

gut feeling

probability of a loss

stock market