question 7 (1 point) the demand function for a new cd is p(x)= - 4x + 24 where p(x) represents the selling…

question 7 (1 point) the demand function for a new cd is p(x)= - 4x + 24 where p(x) represents the selling price, in thousands of dollars, and x is the number of cds sold, in thousands. what is the maximum revenue? revenue = p(x)(x) a) $24 000 b) $20 000 c) $36 000 d) $3000

question 7 (1 point) the demand function for a new cd is p(x)= - 4x + 24 where p(x) represents the selling price, in thousands of dollars, and x is the number of cds sold, in thousands. what is the maximum revenue? revenue = p(x)(x) a) $24 000 b) $20 000 c) $36 000 d) $3000

Answer

Explanation:

Step1: Find revenue function

Revenue $R(x)=p(x)\times x=(-4x + 24)x=-4x^{2}+24x$.

Step2: Identify coefficients for quadratic - formula

For a quadratic function $y = ax^{2}+bx + c$, here $a=-4$, $b = 24$, $c = 0$. The x - value of the vertex of a quadratic function $y=ax^{2}+bx + c$ is $x=-\frac{b}{2a}$.

Step3: Calculate x - value of vertex

$x=-\frac{24}{2\times(-4)}=\frac{-24}{-8}=3$.

Step4: Calculate maximum revenue

Substitute $x = 3$ into the revenue function $R(x)=-4x^{2}+24x$. $R(3)=-4\times3^{2}+24\times3=-4\times9 + 72=-36 + 72 = 36$. Since $x$ is in thousands and $R(x)$ is in thousands of dollars, the maximum revenue is $36000$ dollars.

Answer:

c) $$36000$