Question

Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue R in dollars is

R(p)= -4p^2+4000p

What unit price should be established for the dryer to maximize revenue?

What is the maximum revenue?

Answer 1

Answer: The maximum revenue is $1,000,000.

The function that is given is a quadratic equation and the graph would be an upside down parabola.

Therefore, the maximum revenue would be at the vertex of the parabola.

To find the vertex, we can use the expression -b/2a to find the x-value.

It would be -4000/2(-4) = 500

Now, input 500 for p and you will get a revenue of 1,000,000.

Answer 2

p=$500 is the unit price to get maximum revenue

Maximum revenue = $1,000,000

Explanation:

the revenue R in dollars is:

`R(p)= -4p^2+4000p`

To find out the unit price to get maximum revenue we find out the vertex

In the given quadratic equation a=-4 and b= 4000

Formula to find out the x coordinate of vertex is

`x=(-b)/(2a)`, plug in the values

`x=(-4000)/(2(-4))`

x=500

So p=$500 is the unit price to get maximum revenue

Now we find the maximum revenue . Plug in 500 for p in the given equation

`R(p)= -4p^2+4000p`

`R(500)= -4(500)^2+4000(500)`

R(500)=1000000

Maximum revenue = $1,000,000