Mathew is a financial analyst for a surf board company. He has found an equation for the revenue of selling t-shirts with the company logo to be r= -3p^2 + 60p +1060, where p is the price of the company’s product. What should he use to determine the price of maximum sales?

Respuesta :

Answer: The price of maximum sales is $160

Step-by-step explanation:

This question requires you to find the vertex of this equation. The vertex of a parabola is the point where the parabola crosses its axis of symmetry.

since the coefficient of the [tex]x^2[/tex] term is negative, the vertex will be the highest point on the graph.

this quadratic equation is in standard form: [tex]y = ax^2+bx+c[/tex].

From this, we can derive:

[tex]a = -3[/tex]

[tex]b = 60[/tex]

[tex]c = 1060[/tex]

First, determine the axis of symmetry ([tex]p[/tex] is the variable for the horizontal axis ([tex]x[/tex]) in this instance). This will be our x-coordinate of the vertex.

[tex]p = \frac{-b}{2a}[/tex]

[tex]p = \frac{-(60)}{2(-3)}[/tex]

[tex]p = \frac{-60}{-6}[/tex]

[tex]p=10[/tex]

Then, substitute the axis of symmetry into the function to find the y coordinate of the axis of symmetry. r stands for the variable for the vertical axis in this instance. This will be our y-coordinate of the vertex.

[tex]r = -3(10)^2+60(10)+1060[/tex]

[tex]r = 160[/tex]

As we have determined both the x and y coordinate of the vertex for this equation, we can determine that the maximum point is at [tex](10, 160)[/tex].

the maximum price ([tex]r[/tex]) is 160

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