2) In most businesses, increasing prices of their product can have a negative effect on the number of custome

Question

2) 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.



Given the description above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph you have drawn, and also the domain and range of the entire function excluding unrealistic values. The vertical axis is the number of riders per day, and the horizontal axis is the fare.



Graph:


Graph Type:

Explanation:

Domain:

Range:

Answer 1

revenue = # of riders * amount per rider
x = amount of increase in $0.25 increments
# of riders = 1000 - 50x
amounter per rider = 2.00 + 0.25x
R = (1000 - 50x)*(2.00 + 0.25x) = 2000 + 150x - 12.5x^2
dR/dx = 150 - 25x
x = 6
Fare should be $3.50 to maximize revenue.
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Oh well if you graph fare vs # of riders it'll be a line sloping down.
Domain is from 2.00 to 7.00 and the range is from 1000 down to 0.