SOLUTION: A research study has shown that 500 people attend a tournament when the admission price is $2. In the championship game, the price will be considered for an increase: for every 20c

Question 454469: A research study has shown that 500 people attend a tournament when the admission price is $2. In the championship game, the price will be considered for an increase: for every 20cent increase, 20 fewer people will attend. What price will maximize the revenue? What is the value of the maximum revenue?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
A research study has shown that 500 people attend a tournament when the admission price is $2. In the championship game, the price will be considered for an increase: for every 20cent increase, 20 fewer people will attend. What price will maximize the revenue? What is the value of the maximum revenue?
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Let x = the number of 20 cent increases in price
Then the equation for the revenue will be:
R = (500 - 20x)(2 + 0.2x)
Expanding and collecting terms gives:
R = 1000 + 60x - 4x^2
The revenue will be maximized where dR/dx = 0:
dR/dx = 0 = 60 - 8x
Solving for x gives x = 7.5
So the price which maximizes revenue is 2 + 7.5*0.2 = 3.5 = $3.50
So the maximum revenue is 3.5*(500 - 20*7.5) = $1225

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