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Answer:<u><em> Price per ticket should be charged in order to maximize revenue is $15.</em></u>
<u><em>70000 people will attend at this price.</em></u>
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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 Average no. of people that watch the game + Additional money spent
Revenue [R(x)] = (24 - 3x)(40000 + 10000x) + 6(40000 + 10000x)
On solving the above equation we get ,
Revenue [R(x)] = -30000 + 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
<u><em>Thus, the price per ticket that should be charged in order to maximize revenue is (24 - 33 = 24 - 9 = $15)</em></u>
<u><em>People that will attend at this price = (40000 + 100003) = 70000</em></u>