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Sagot :
The profit function can be gotten using the formula below:
[tex]P(x)=R(x)-C(x)[/tex]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:
[tex]\begin{gathered} R(x)=425x \\ C(x)=315x+15600 \end{gathered}[/tex]Therefore, the profit function is:
[tex]\begin{gathered} P(x)=425x-(315x+15600) \\ P(x)=425x-315x-15600 \\ P(x)=110x-15600 \end{gathered}[/tex]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:
[tex]\begin{gathered} 50000=110x-15600 \\ 110x=50000+15600 \\ 110x=65600 \\ x=\frac{65600}{110} \\ x=596.4 \end{gathered}[/tex]Therefore, the number of kayaks that must be sold is approximately 597 kayaks to make $50,000 in profits.
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