Two models are used to predict monthly revenue for a new sports drink. In each model, x is the number of $1 – price increases from the original $2 per bottle price.
Model A : f(x)= -12.5 x²+75x+200
Model B:

The correct answer is: 312.5

a. Identify the price you would set for each model to maximize monthly revenue. Explain.
Solution:- For maximizing the monthly revenue we have to find the vertex of  the both curves .
For Model A :-
In f(x)= -12.5 x²+75x+200,  a= -12.5, b= 75, and c= 200. So, the equation for the axis of symmetry is given by
x = −(75)/2(-12.5)
x = -75/-25
x = 3
The equation of the axis of symmetry for f(x)= -12.5 x²+75x+200 is x = 3.
The x coordinate of the vertex is the same:
h = 3
The y coordinate of the vertex is :
k = f(h)
k = -12.5h²+75h+200
k = -12.5(3)² + 75(3) +200
k = -112.5 + 225 + 200
k = 312.5
Therefore, the vertex is (3 , 312.5)
The maximum revenue of model A will be the y-coordinate of vertex = 312.5
For model B:-
From the given graph we can analyse that the maximum revenue is 360 at the price of 4.
b.    A Third model includes the points (9, 605), (8,600),    (10,600), (7,585) and (11,585). What price maximizes revenue according to this model ? Explain.
Solution:- We have