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A retailer spends [tex]$\$[/tex] 500[tex]$ per month to keep its online shop active and updated. The store acquires shirts at a marginal cost of $[/tex]\[tex]$ 5$[/tex] per shirt. Each shirt sells for a marginal benefit of [tex]$\$[/tex] 10[tex]$ per shirt.

What is the minimum number of shirts the retailer needs to sell in order to pay for all its costs in a month?

\begin{tabular}{|l|l|l|l|}
\hline Quantity of shirts sold & Marginal cost & Total cost & Marginal benefit \\
\hline 0 & $[/tex]\[tex]$ 0$[/tex] & [tex]$\$[/tex] 500[tex]$ & $[/tex]\[tex]$ 0$[/tex] \\
\hline 25 & [tex]$\$[/tex] 125[tex]$ & $[/tex]\[tex]$ 625$[/tex] & [tex]$\$[/tex] 250[tex]$ \\
\hline 50 & $[/tex]\[tex]$ 250$[/tex] & [tex]$\$[/tex] 750[tex]$ & $[/tex]\[tex]$ 500$[/tex] \\
\hline 75 & [tex]$\$[/tex] 375[tex]$ & $[/tex]\[tex]$ 875$[/tex] & [tex]$\$[/tex] 750[tex]$ \\
\hline 100 & $[/tex]\[tex]$ 500$[/tex] & [tex]$\$[/tex] 1,000[tex]$ & $[/tex]\[tex]$ 1,000$[/tex] \\
\hline 125 & [tex]$\$[/tex] 625[tex]$ & $[/tex]\[tex]$ 1,125$[/tex] & [tex]$\$[/tex] 1,250$ \\
\hline
\end{tabular}

A. 125

B. 25

C. 100

D. 75

Sagot :

GinnyAnswer
To determine the minimum number of shirts the retailer needs to sell to cover all its costs in a month, we need to take the following steps:

1. Understand the costs and revenues:
- Fixed monthly cost: \[tex]$500 - Marginal cost per shirt: \$[/tex]5
- Marginal benefit per shirt: \[tex]$10 2. Calculate the net profit per shirt: - Net profit per shirt = Marginal benefit per shirt - Marginal cost per shirt - Net profit per shirt = \$[/tex]10 - \[tex]$5 = \$[/tex]5

3. Find the minimum number of shirts that need to be sold to cover the fixed monthly cost:
- Let [tex]\( x \)[/tex] be the number of shirts that need to be sold.
- Total profit from selling [tex]\( x \)[/tex] shirts should equal the fixed cost.
- Net profit from [tex]\( x \)[/tex] shirts = Fixed monthly cost
- [tex]\( 5x = 500 \)[/tex]

4. Solve for [tex]\( x \)[/tex]:
- [tex]\( x = \frac{500}{5} \)[/tex]
- [tex]\( x = 100 \)[/tex]

Therefore, the retailer needs to sell a minimum of 100 shirts to cover all its costs in a month.

The correct answer is:

C. 100
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