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The revenue function for a bicycle shop is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=200−0.4x is the unit price. Find the maximum revenue.

User Meer
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1 Answer

4 votes

Answer:

maximum revenue is 25000

Explanation:

The revenue function for a bicycle shop is given by R(x)=x⋅p(x)

Given
p(x)= 200-0.4x


R(x)=x \cdot p(x)

Plug in p(x) in R(x)


R(x)=x \cdot 200-0.4x


R(x)=200x-0.4x^2

Now find out the vertex using formula x=-b/2a

a= -0.4, b=200


x=(-b)/(2a) =(-200)/(2(-.4)) =250

Plug in 250 for x in R(x)


R(x)=200x-0.4x^2


R(x)=200(250)-0.4(250)^2=25000

So maximum revenue is 25000

User Lollercoaster
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