Problema Solution
During the off-season, Six Flags charges $12 per day. The amusement park averages 1000 patrons per day. The company is considering a $2 increase. However, for each $2 increase, they lose 100 patrons. What is the ideal admission?
Answer provided by our tutors
we need to find the maximum of the function:
y = (12 + 2x)(1000 - 100x), where x represents the number of times that the $2 increase happened
y = -200x^2 + 800x + 12000
since the quotient in front of x^2 is negative the function has a maximum in the vertex for
x = -b/(2a) where a = -200, b = 800
x = -800/(2*(-200))
x = 2
the ideal admission is: 12 + 2*2 = $16.