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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?

User Cisco
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1 Answer

1 vote

Answer:

$500 will give the company the maximum revenue

Explanation:

Given


r(x) = x (1000 - 2x)

Required

Price to generate maximum revenue

We have:


r(x) = x (1000 - 2x)

Open bracket


r(x) = 1000x - 2x^2

Rewrite as:


r(x) = - 2x^2 + 1000x

The maximum value of x is calculated using:


x = -(b)/(2a)

Where:


f(x) = ax^2 + bx + c

So:


a \to -2


b = 1000


c = 0


x = -(b)/(2a)


x = -(1000)/(-2)


x = (1000)/(2)


x = 500

User MDroidd
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