Question

Suppose the profit function for a company selling x items if a product is given by p(x)=-6x^2+360x-2500.

what is number of units will maximize the company's profit for this product?
what is the maximum profit?

Answer 1

$2700

Explanation:

The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -6 and b = 360, so we have:

x = -360/(2*(-6)) = 30

Therefore, the company will maximize its profit by selling 30 units of the product.

p(x) = -6x^2 + 360x - 2500

(x = 30 )

p(30) = -6(30)^2 + 360(30) - 2500 = 2700

So, the maximum profit for the company is $2700.