Respuesta :
Answer: Price per ticket should be charged in order to maximize revenue is $15.
70000 people will attend at this price.
Explanation:
Let 'x' represent the decrease .
Using the given information,
Price per ticket = 24 - 3x
Average no. of people that watch the game = 40000 + 10000x
Additional money spent by every person = 6(40000 + 10000x)
Revenue [R(x)] = Price per ticket [tex]\times[/tex] Average no. of people that watch the game + Additional money spent
Revenue [R(x)] = (24 - 3x)[tex]\times[/tex](40000 + 10000x) + 6(40000 + 10000x)
On solving the above equation we get ,
Revenue [R(x)] = -30000[tex]x^{2}[/tex] + 180000x + 1200000
In order to find the critical point we'll differentiate the following with respect to x;
R'(x) = -60000x + 180000
∵ R'(x) = 0
x = 3
Thus, the price per ticket that should be charged in order to maximize revenue is (24 - 3[tex]\times[/tex]3 = 24 - 9 = $15)
People that will attend at this price = (40000 + 10000[tex]\times[/tex]3) = 70000
