Answer:
(a) [tex]p(x) = 17-\frac{x}{3,500}[/tex]
(b) $8.50
Step-by-step explanation:
(a) The slope of the demand function, p(x), is determined by:
[tex]m=\frac{11-9}{21,000-28,000}=-\frac{1}{3,500 }[/tex]
Applying the point (21,000; 11) to the general linear equation formula gives us the demand function:
[tex]p(x) - 11 = -\frac{1}{3,500}*(x-21,000)\\p(x) = 17-\frac{x}{3,500}[/tex]
(b) The revenue function, r(x), is given by:
[tex]r(x) =x*p(x) = 17x-\frac{x^2}{3,500}[/tex]
The value of x for which the derivate of the revenue function is zero gives us the attendance for which revenue is maximized:
[tex]\frac{dr(x)}{dx} =0= 17-\frac{2x}{3,500}\\x=29,750[/tex]
At an attendance of 29,750, the price is:
[tex]p = 17-\frac{29,750}{3,500}\\p=\$8.50[/tex]
Tickets should be set at a price of $8.50.
