Posted by **Debo** on Friday, October 4, 2013 at 12:30pm.

a City's transit authority serves 178500 communters daily when the fare is $1.90. Market research has determined that every penny decrease in the fare will result in 1,050 new riders. what fare will maximize revenue?

- Algebra -
**Steve**, Friday, October 4, 2013 at 12:45pm
revenue = #riders * fare

= (178500+1050(190-x))(.01x) for x<=190

that's just a parabola with vertex at x=180.

- Algebra -
**Reiny**, Friday, October 4, 2013 at 12:49pm
number of penny decreases ---- n

cost of fare = 190-n

number of riders = 178500 + 1050n

revenue = R = (190-n)(178500+1050n)

P' = (190-n)(1050) + (178500 + 1050n)(-1)

= 0 for a max of P

178500 + 1050n = 1050(190-n)

divide by 1050

170 + n = 190-n

2n = 20

n = 10

the fare should be 190+10 = 200

or it should be $ 2.00

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