charlotte - mecklenburg schools (cms) is going to host a superhero \dinner and a movie\ fundraiser at a…

charlotte - mecklenburg schools (cms) is going to host a superhero \dinner and a movie\ fundraiser at a local theater. tickets will be for dinner and a screening of wakanda forever. they hire you as a consultant to help set the selling price of the tickets. you analyze the costs and consumer demands and arrive at a function for the profit, $p(x)=-x^{2}+90x - 100$, where $x$ represents the price of a ticket for dinner and watching wakanda forever. according to the function given (and your approximation in the previous question), what is the maximum profit that cms can make? approximately $\\$□$

charlotte - mecklenburg schools (cms) is going to host a superhero \dinner and a movie\ fundraiser at a local theater. tickets will be for dinner and a screening of wakanda forever. they hire you as a consultant to help set the selling price of the tickets. you analyze the costs and consumer demands and arrive at a function for the profit, $p(x)=-x^{2}+90x - 100$, where $x$ represents the price of a ticket for dinner and watching wakanda forever. according to the function given (and your approximation in the previous question), what is the maximum profit that cms can make? approximately $\\$□$

Answer

Explanation:

Step1: Identify the function type

The profit function $P(x)=-x^{2}+90x - 100$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-1$, $b = 90$, $c=-100$.

Step2: Find the x - value of the vertex

The x - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $a=-1$ and $b = 90$ into the formula, we get $x=-\frac{90}{2\times(-1)}=\frac{-90}{-2}=45$.

Step3: Find the maximum profit

Substitute $x = 45$ into the profit function $P(x)$. So $P(45)=-(45)^{2}+90\times45-100=-2025 + 4050-100=1925$.

Answer:

1925