Answer:
See Explanation
Step-by-step explanation:
Given
See attachment for complete question
First, we determine the cost function for all the three rides.
Ride A
From the graph, we have the following points
[tex](x_1,y_1) = (0,8)[/tex]
[tex](x_2,y_2) = (2,12)[/tex]
Calculate slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{12-8}{2-0}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m =2[/tex] --- This represents the rate per ride
The equation is the calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 2(x - 0) + 8[/tex]
[tex]y = 2(x) + 8[/tex]
[tex]y = 2x + 8[/tex]
So, the cost function is:
[tex]C(x) =2x + 8[/tex]
Calculate the cost of admission i.e. x=0
[tex]C(0) = 2*0+8 = 8[/tex]
So, we have:
[tex]C(0) = 8[/tex] --- Admission Charge
[tex]C(x) =2x + 8[/tex] --- Cost function
[tex]m =2[/tex] --- Rate per ride
Ride B
From the table, we have the following points
[tex](x_1,y_1) = (0,12)[/tex]
[tex](x_2,y_2) = (4,15)[/tex]
Calculate slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{15-12}{4-0}[/tex]
[tex]m = \frac{3}{4}[/tex]
[tex]m = 0.75[/tex] --- This represents the rate per ride
The equation is the calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 0.75(x - 0) + 12[/tex]
[tex]y = 0.75(x) + 12[/tex]
[tex]y = 0.75x + 12[/tex]
So, the cost function is:
[tex]C(x) = 0.75x + 12[/tex]
Calculate the cost of admission i.e. x=0
[tex]C(0) = 0.75*0 + 12=12[/tex]
So, we have:
[tex]C(0) =12[/tex] --- Admission Charge
[tex]C(x) = 0.75x + 12[/tex] --- Cost function
[tex]m = 0.75[/tex] --- Rate per ride
Ride C
No additional fee;
So, the cost function is;
[tex]C(x) = 30[/tex]
In summary, we have:
Ride A
[tex]C(x) =2x + 8[/tex] --- Cost function
[tex]m =2[/tex] --- Rate per ride
Ride B
[tex]C(x) = 0.75x + 12[/tex] --- Cost function
[tex]m = 0.75[/tex] --- Rate per ride
Ride C
[tex]C(x) = 30[/tex] --- Cost function
By comparison
Ride A has the highest rate per ride of (#2), followed by ride B with a rate of #0.75 per ride.
Ride C has no charges per ride
The impact on the total cost is that:
Ride A: People that opt for ride A will pay the least to get admitted (i.e #8) but they pay the most (i.e. #2) per each ride they take
Ride B: People that opt for ride B will pay #12 to get admitted, but they pay 0.75 per each ride they take
For A and B, the overall cost depends on the number of rides taken.
Ride C: Irrespective of the number of rides taken, people that opt for ride C will pay the same flat fee of #30
