Question

Zacaria's kayaks store annual rent and fixed cost are $ 15,600. The variable cost each kayak old is $315 and the price of each kayak is $425.e. What is the number of kayaks that must be sold to obtain $ 50,000 in the profits?

Answer 1

The profit function can be gotten using the formula below:

`P(x)=R(x)-C(x)`

where R(x) is the revenue function and C(x) is the cost function.

As previously calculated, the revenue and cost functions are given to be:

`\begin{gathered} R(x)=425x \\ C(x)=315x+15600 \end{gathered}`

Therefore, the profit function is:

`\begin{gathered} P(x)=425x-(315x+15600) \\ P(x)=425x-315x-15600 \\ P(x)=110x-15600 \end{gathered}`

The profit to be made is $50,000. Equating the profit function to this amount, we can get the number of kayaks required. This is shown below:

`\begin{gathered} 50000=110x-15600 \\ 110x=50000+15600 \\ 110x=65600 \\ x=(65600)/(110) \\ x=596.4 \end{gathered}`

Therefore, the number of kayaks that must be sold is approximately 597 kayaks to make $50,000 in profits.