89. Going on a tour. A group of students plans a tour. The charge per student is \( \$ 72 \) if \( 20 \) students go on the trip. If more than \( 20 \) students participate, the charge per student is reduced by \( \$ 2 \) times the number of students over \( 20 . \) Find the number of students that will furnish the maximum revenue. What is the maximum revenue?
Pregunta
Answer
\(f(x) = (20+ x)(72- 2x) = 1440+ 32x- 2x^2\) ,
putting f'(x) = 0 ,
\(f'(x) = 32- 4x = 0 , x = 8\) , hence 28 students , revenue = $1568
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