kyleemarie2003
contestada

A company's profit is described by the equation P(x)=-5x^2+300x+15,000
Where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?

A)$20

B)$30

C$50

D$60

Respuesta :

altavistard
P(x)=-5x^2+300x+15,000 is the equation of a parabola and represents profit.  Its graph opens down.  Our job is to find the x-coordinate of the vertex (which is the x-coord of the maximum profit) and then the corresponding y-value.

The formula x = -b / (2a) will produce that x-coordinate:

        -(300)
x = ------------ = 30
         2(-5)

When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500  (answer)

The company charge for the product to generate a maximum profit is $30. Then the correct option is B.

What is differentiation?

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

A company's profit is described by the equation

[tex]\rm P(x)=-5x^2+300x+15000[/tex]

Where x is the price in dollars that the company charges for its product.

Differentiate the equation with respect to x.

[tex]\rm \dfrac{dP(x)}{dx}=-10x+300[/tex]

For the maximum price

[tex]\rm \dfrac{dP(x)}{dx} = 0\\[/tex]

Then we have

[tex]\begin{aligned} \rm -10x+300 &= 0\\\\\rm 10x &= 300\\\\\rm x &= 30 \end{aligned}[/tex]

Then the company charge for the product to generate the maximum profit is 30 dollars for each.

More about the differentiation link is given below.

https://brainly.com/question/24062595

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