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A carpenter finds that if she charges p dollars for a chair, she sells 600 – 3p of them each year.

How much should she charge to maximize her annual revenue?

Respuesta :

calculista

Answer:

p=$100

Step-by-step explanation:

Let

y -----> annual revenue

p ----> the charge in dollars for a chair

we know that

The revenue is equal to the number of chairs multiplied by the charge for one chair

so

[tex]y=(600-3p)p[/tex]

[tex]y=600p-3p^2[/tex]

This is the equation of a vertical parabola open downward.

The vertex is a maximum

using a graphing tool

The vertex is the point (100,30,000)

That means

The maximum revenue is y=$30,000

when the carpenter charge $100 for a chair

Ver imagen calculista
raphealnwobi

The revenue is maximum when a fee of $100 is charged per chair.

Equation

An equation is an expression used to show the relationship between two or more variables and numbers.

Revenue is the product of the price per item and the total number of items.

Hence:

Revenue (R) = Price * number of item

R = p * 600 - 3o

R = 600p - 3p²

Maximum revenue is at R' = 0:

R' = 600 - 6p

6p = 600

p = 100

The revenue is maximum when a fee of $100 is charged per chair.

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