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To calculate the per night break$-$even point in dollars for the St$.$ Cloud Theatre Company, we need to consider the total fixed costs and the contribution margin.

Let's calculate the contribution margin for each item:

Soft Drink:

Selling Price: $$1\mathrm{.}20$

Variable Cost: $$0\mathrm{.}70+10\%$ waste allowance $=$ $$0\mathrm{.}77$

Contribution Margin per unit $=$ Selling Price $-$ Variable Cost $=$ $$1\mathrm{.}20-$ $$0\mathrm{.}77=$ $$0\mathrm{.}43$

Wine:

Selling Price: $$2\mathrm{.}00$

Variable Cost: $$0\mathrm{.}95+10\%$ waste allowance $=$ $$1\mathrm{.}045$

Contribution Margin per unit $=$ Selling Price $-$ Variable Cost $=$ $$2\mathrm{.}00-$ $$1\mathrm{.}045=$ $$0\mathrm{.}955$

Coffee:

Selling Price: $$1\mathrm{.}50$

Variable Cost: $$0\mathrm{.}40+10\%$ waste allowance $=$ $$0\mathrm{.}44$

Contribution Margin per unit $=$ Selling Price $-$ Variable Cost $=$ $$1\mathrm{.}50-$ $$0\mathrm{.}44=$ $$1\mathrm{.}06$

Candy:

Selling Price: $$1\mathrm{.}20$

Variable Cost: $$0\mathrm{.}35+10\%$ waste allowance $=$ $$0\mathrm{.}385$

Contribution Margin per unit $=$ Selling Price $-$ Variable Cost $=$ $$1\mathrm{.}20-$ $$0\mathrm{.}385=$ $$0\mathrm{.}815$

Now, let's calculate the weighted average contribution margin $($weighted by the percentage of revenue for each item$)$:

Weighted Average Contribution Margin

$=$

$($

$26$

$\%$

$\backslash$times

Contribution Margin for Soft Drink

$)$

$+$

$($

$26$

$\%$

$\backslash$times

Contribution Margin for Wine

$)$

$+$

$($

$30$

$\%$

$\backslash$times

Contribution Margin for Coffee

$)$

$+$

$($

$18$

$\%$

$\backslash$times

Contribution Margin for Candy

$)$

Weighted Average Contribution Margin$=(26\%\backslash$times Contribution Margin for Soft Drink$)+(26\%\backslash$times Contribution Margin for Wine$)+(30\%\backslash$times Contribution Margin for Coffee$)+(18\%\backslash$times Contribution Margin for Candy$)$

Finally, we can use the contribution margin to calculate the break$-$even point in dollars using the formula:

Break$-$Even Point

$=$

Fixed Costs

Weighted Average Contribution Margin

Break$-$Even Point$=$

Weighted Average Contribution Margin

Fixed Costs

$$

Given that labor cost is $$280\mathrm{.}00,$ booth rental is $$60\mathrm{.}00$ per booth $($there are $5$ booths$),$ and considering the waste allowance, the fixed costs are:

Fixed Costs

$=$

Labor Cost

$+$

$($

Number of Booths

$\backslash$times

Booth Rental

$)$

Fixed Costs$=$Labor Cost$+($Number of Booths$\backslash$times Booth Rental$)$

$\backslash$text$\{$Fixed Costs$\}=$ $$280\mathrm{.}00+(5\backslash$times $$60\mathrm{.}00)=$ $$280\mathrm{.}00+$ $$300\mathrm{.}00=$ $$580\mathrm{.}00$

Now, plug in the values to find the break$-$even point:

$\backslash$text$\{$Break$-$Even Point$\}=\backslash$frac$\{$$$580\mathrm{.}00\}\{\backslash$text$\{$Weighted Average Contribution Margin$\}\}$

Please calculate the weighted average contribution margin and then use the formula to find the break$-$even point.

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