The profit (in thousands of dollars) of a company is represented as P=-5x^2+1,000+5,000, where P represents that profit and x represents the amount spent on marketing (in thousands of dollars). How much spending in the thousands will be directed toward marketing to achieve the maximum profit?

Answer 1

To find the maximum profit, we need to find the value of x that maximizes the profit function P = -5x^2 + 1000x + 5000.

The maximum value occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, where a = -5 and b = 1000.

x = -1000 / (2*(-5))
x = -1000 / (-10)
x = 100

Therefore, the company should spend $100,000 on marketing to achieve the maximum profit.

Answer 2

That's wrong, it's not $100,000, try again please.

Answer 3

Apologies for the mistake. Let's find the correct amount of spending on marketing to achieve the maximum profit.

The profit function is given by P = -5x^2 + 1000x + 5000.

To find the maximum profit, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, where a = -5 and b = 1000.

x = -1000 / (2*(-5))
x = -1000 / (-10)
x = 100

Therefore, the company should spend $100,000 on marketing to achieve the maximum profit.