question bittermans finest bakery is a restaurant down the street from pauls new café. managers at…

question bittermans finest bakery is a restaurant down the street from pauls new café. managers at bittermans have seen a decline in customers lately, so they developed some new pricing options. these equations describe the cost and revenue associated with the sales of their signature dish over the course of a week: r(x)= - 175x² + 4,200x c(x)= - 665x + 27,300 select the correct answer from each drop - down menu. bittermans employees jeff and rochelle each wrote down what they thought was the profit function from the given cost and revenue. jeff: p(x)= - 175x² + 3,535x - 27,300 rochelle: p(x)= - 175x² + 4,865x - 27,300 wrote the correct profit equation. the maximum profit of $ for this dish can be earned when its priced at $

question bittermans finest bakery is a restaurant down the street from pauls new café. managers at bittermans have seen a decline in customers lately, so they developed some new pricing options. these equations describe the cost and revenue associated with the sales of their signature dish over the course of a week: r(x)= - 175x² + 4,200x c(x)= - 665x + 27,300 select the correct answer from each drop - down menu. bittermans employees jeff and rochelle each wrote down what they thought was the profit function from the given cost and revenue. jeff: p(x)= - 175x² + 3,535x - 27,300 rochelle: p(x)= - 175x² + 4,865x - 27,300 wrote the correct profit equation. the maximum profit of $ for this dish can be earned when its priced at $

Answer

Explanation:

Step1: Recall profit - revenue - cost formula

The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$. Given $R(x)= - 175x^{2}+4200x$ and $C(x)=-665x + 27300$. So, $P(x)=(-175x^{2}+4200x)-(-665x + 27300)$.

Step2: Simplify the profit - function expression

$P(x)=-175x^{2}+4200x + 665x-27300=-175x^{2}+4865x - 27300$. So Rochelle wrote the correct profit equation.

Step3: Find the x - value for maximum of quadratic function

For a quadratic function $y = ax^{2}+bx + c$ ($a\neq0$), the x - value of the vertex (where maximum or minimum occurs) is given by $x=-\frac{b}{2a}$. For $P(x)=-175x^{2}+4865x - 27300$, $a=-175$ and $b = 4865$. $x=-\frac{4865}{2\times(-175)}=\frac{4865}{350}=\frac{973}{70}\approx13.9$.

Step4: Find the maximum profit value

Substitute $x = \frac{973}{70}$ into the profit function $P(x)$. $P(\frac{973}{70})=-175\times(\frac{973}{70})^{2}+4865\times\frac{973}{70}-27300$. $P(\frac{973}{70})=-175\times\frac{946729}{4900}+\frac{4733645}{70}-27300$. $P(\frac{973}{70})=-\frac{165677575}{4900}+\frac{33135515}{4900}-\frac{133770000}{4900}$. $P(\frac{973}{70})=\frac{-165677575 + 33135515-133770000}{4900}=\frac{-266312060}{4900}=10981.125$.

Answer:

Rochelle; 10981.125; 13.9