Suppose that a small candy store makes$$ Valentine's Day gift boxes that cost $$$$10\mathrm{.}75$ and sell for $$$$16\mathrm{.}00.$ In the$$ past, at least $40$ boxes have been sold by$$ Valentine's Day, but the actual amount is$$ uncertain, and the owner has often run short or made too many. After the$$ holiday, any unsold boxes are discounted$50\%$ and are eventually sold. Set up and run a Monte Carlo simulation assuming that demand is triangular with minimum valueequals$40,$ maximum valueequals$50,$ and most likely valueequals$47.$ Find the distribution of profit for order quantities between $40$ and $50$ to identify the best order quantity. Use $20$ simulation trials.

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Part $1$

Say the values of the selling$$ price, cost, and discount price are entered in cells$$ B$6,$ B$7,$ and$$ B$8,$ respectively, and the$$ demand, purchase$$ quantity, quantity$$ sold, and surplus quantity are entered in cells$$ B$12,$ B$13,$ B$15,$ and$$ B$16,$ respectively.$$ Then, for the Monte Carlo$$ simulation, the quantity sold is $=$

$$

MAX

MIN

$($B

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enter your response here$,$B

$$

enter your response here$),$ the surplus quantity is $=$

$$

MAX

MIN

$($

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enter your response here$,$B

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$$

$-$

$+$

$/$

$*$

B

$$

enter your response here$),$ and the profit is $=$B$15*$B

$$

enter your response here$+$B$16*$B

$$

enter your response here$-$B$13*$B

$$

enter your response here.

$($Type whole numbers. Use ascending$$ order.$)$

Part $2$

Say the Monte Carlo simulation produced the provided simulation trial results. Use these results to determine the best order quantity.

The best order quantity is

$$

enter your response here.

$($Type a whole$$ number.$)$