Question 784955
A bus company carries about 40 000 riders per day for a fee of $1.00.
 A survey indicates that if the fare is decreased, the number of riders will increase by 2500 for every 5 cents decrease.
What fare will result in the greatest reverse? 
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I'm not sure what "reverse" means here. Perhaps you mean "revenue".
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Let x = number of 5 cent decreases and no. of 2500 passenger increases
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Find the fare that gives maximum revenue
Revenue = fare * no. of passengers
R(x) = (1-.05x)(40000+2500x)
FOIL
R(x) = 40000 + 2500x - 2000x - 125x^2
Write as a quadratic equation
y = -125x^2 + 500x + 40000
Max y occurs at the axis of symmetry, find that using x = -b/(2a)
x = {{{(-500)/(2*-125)}}}
x = {{{(-500)/(-250)}}}
x = +2 fare decreases $.90 fare
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That would give a increase in passengers of 5000
Max revenue: .90 *(40000+5000) = $40,500 max revenue
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You can prove this to yourself, find the revenue using $.85 and $.95