Question 80224: If someone could show me how to get started - I would so greatful! Here is the whole problem:
In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.
Part One:
Graph function,identify the graph of the function (line,parabola, hyperbola, exponential), find the slope of the graph, find the price at which there will be no more riders,a nd find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare.
(I have never been could with word problems - I just need help getting started)
Part Two:
The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?
( Must to first part to do this part)
Part Three:
If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?
( Must do the rest in order to do this part)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.
Function is Income = (# of riders)(price paid):
Let x = # of days
Income = (1000-50x)(2.00+0.25x)
I(x) = -(25/2)x^2+150x+2000
Part One:
Graph function
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identify the graph of the function (parabola),
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find the slope of the graph: slope = -25x-150
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find the price at which there will be no more riders:
No riders means 1000-50x=0
50x=10000 implies x=20
Price when x=20 is $2 + 20*0.25=$7
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find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare.
You need a set of points of the form (2+0.25x,1000-50x):
such as (2,1000), (1.75.25,1050),(1.50,1100)...(0,1400)
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Part Two:
The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day? Answered already above---#=1400
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Part Three:
If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?
(2,1000), (2.25,950), (2.50,900)....(2+20*0.25,1000-20*50)=(7,0)
No one will ride the bus when the price is $7
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Cheers,
Stan H.
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