Answer:
a) p(x)=-0.0006x +21.6
b) $10.80
Step-by-step explanation:
a) Assuming that p(x) is linear, the slope can be found by:
[tex]m=\frac{\$9-\$6}{21000-26000} \\m=-0.0006[/tex]
Applying the point (21000; $9) to the general linear equation gives us the demand function:
[tex](p-p_0)=m(x-x_0)\\(p-9)=-0.0006(x-21,000)\\p(x)=-0.0006x +21.6[/tex]
b) Revenue is given by the number of tickets sold multiplied by the price, the revenue function is:
[tex]R(x) = xp(x)\\R(x) = -0.0006x^2 +21.6x[/tex]
The value of x for which the revenue function's derivate is zero is the number of spectators that yield the maximum revenue:
[tex]\frac{dR(x)}{dx} = -0.0012x +21.6 = 0\\x=\frac{21.6}{0.0012}\\x= 18,000[/tex]
At x = 18,000, tickets price are:
[tex]p(18,000)=-0.0006*18,000 +21.6\\p = \$10.80[/tex]
