2\nselect the correct answer.\nthese are the cost and revenue functions for a product line of cat food sold…

2\nselect the correct answer.\nthese are the cost and revenue functions for a product line of cat food sold in 7 - pound bags at a single pet store:\n$r(x)=700x - 11.3x^{2}$\n$c(x)=8068 - 34.25x$\nbased on these functions, what is the maximum profit that can be made?\na. $1,737.82\nb. $3,859.50\nc. $8,068.00\nd. $10,840.71

2\nselect the correct answer.\nthese are the cost and revenue functions for a product line of cat food sold in 7 - pound bags at a single pet store:\n$r(x)=700x - 11.3x^{2}$\n$c(x)=8068 - 34.25x$\nbased on these functions, what is the maximum profit that can be made?\na. $1,737.82\nb. $3,859.50\nc. $8,068.00\nd. $10,840.71

Answer

Explanation:

Step1: Define the profit function

The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$. So, $P(x)=(700x - 11.3x^{2})-(8068 - 34.25x)=- 11.3x^{2}+734.25x - 8068$.

Step2: Find the x - value of the vertex

For a quadratic function $y = ax^{2}+bx + c$, the x - value of the vertex is $x=-\frac{b}{2a}$. Here, $a=-11.3$ and $b = 734.25$. So, $x=-\frac{734.25}{2\times(-11.3)}=\frac{734.25}{22.6}\approx32.5$.

Step3: Find the maximum profit

Substitute $x = 32.5$ into the profit function $P(x)$. $P(32.5)=-11.3\times(32.5)^{2}+734.25\times32.5 - 8068$ $=-11.3\times1056.25+23863.125 - 8068$ $=-11935.625+23863.125 - 8068$ $=3859.5$

Answer:

B. $$3,859.50$