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Easy

Question

# 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 x^{2}+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 x^{2}+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 x^{2}+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 = -12.5h^{2}+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

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