question 18 (1 point) the demand function for a new comic book is p(x)= - 5x + 30 where p(x) represents the…

question 18 (1 point) the demand function for a new comic book is p(x)= - 5x + 30 where p(x) represents the selling price, in thousands of dollars, and x is the number of comic books sold, in thousands. what is the maximum revenue? revenue = p(x)(x) a) $50 000 b) $40 000 c) $30 000 d) $45 000

question 18 (1 point) the demand function for a new comic book is p(x)= - 5x + 30 where p(x) represents the selling price, in thousands of dollars, and x is the number of comic books sold, in thousands. what is the maximum revenue? revenue = p(x)(x) a) $50 000 b) $40 000 c) $30 000 d) $45 000

Answer

Explanation:

Step1: Write revenue function

Revenue $R(x)=p(x)\times x=(- 5x + 30)x=-5x^{2}+30x$.

Step2: Identify coefficients for quadratic - formula

For a quadratic function $y = ax^{2}+bx + c$, in $R(x)=-5x^{2}+30x$, $a=-5$, $b = 30$, $c = 0$. The vertex of a quadratic function $y=ax^{2}+bx + c$ has its $x$ - coordinate at $x=-\frac{b}{2a}$.

Step3: Find the value of $x$ for maximum revenue

$x=-\frac{30}{2\times(-5)}=\frac{-30}{-10}=3$.

Step4: Calculate the maximum revenue

Substitute $x = 3$ into the revenue function $R(x)=-5x^{2}+30x$. $R(3)=-5\times3^{2}+30\times3=-5\times9 + 90=-45 + 90 = 45$. Since $p(x)$ and $x$ are in thousands, the maximum revenue is $45000$ dollars.

Answer:

d) $45000$