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A company finds that if it charges x dollars for a cell phone, it can expect to sell 1,000−2x phones. The company uses the function r defined by r(x)=x⋅(1,000−2x) to model the expected revenue, in dollars, from selling cell phones at x dollars each. At what price should the company sell their phones to get the maximum revenue?

Respuesta :

MrRoyal

Answer:

$500 will give the company the maximum revenue

Step-by-step explanation:

Given

[tex]r(x) = x (1000 - 2x)[/tex]

Required

Price to generate maximum revenue

We have:

[tex]r(x) = x (1000 - 2x)[/tex]

Open bracket

[tex]r(x) = 1000x - 2x^2[/tex]

Rewrite as:

[tex]r(x) = - 2x^2 + 1000x[/tex]

The maximum value of x is calculated using:

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

Where:

[tex]f(x) = ax^2 + bx + c[/tex]

So:

[tex]a \to -2[/tex]

[tex]b = 1000[/tex]

[tex]c = 0[/tex]

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

[tex]x = -\frac{1000}{-2}[/tex]

[tex]x = \frac{1000}{2}[/tex]

[tex]x = 500[/tex]

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