Respuesta :
The profit made is calculated as:
[tex]Profit=Revenue-\text{Costs}[/tex]Revenue:
The revenue cost on each dozen caps is $15. If there are x dozen caps, then the revenue will be:
[tex]Revenue=15x[/tex]Costs:
The costs are divided into fixed cost and variable cost.
The fixed cost is $10000.
The variable cost is $5 per dozen caps. Therefore, for x dozen caps, it will be:
[tex]\Rightarrow5x[/tex]Hence, the total costs will be:
[tex]C(x)=(10000+5x)[/tex]Profit Function:
Given the revenue and costs gotten, we have the profit function to be:
[tex]\begin{gathered} P(x)=15x-(10000+5x) \\ P(x)=15x-5x-10000 \\ P(x)=10x-10000 \end{gathered}[/tex]The profit function is:
[tex]P(x)=10x-10000[/tex]Break-even Point:
The break-even point is the point at which total revenue equals total costs or expenses.
Therefore, the break-even point will be:
[tex]Revenue=\text{ Costs}[/tex]Hence,
[tex]\begin{gathered} 15x=10000+5x \\ 15x-5x=10000 \\ \frac{10x}{10}=\frac{10000}{10} \\ x=1000 \end{gathered}[/tex]The break-even point is after the sale of 1000 dozen caps.
