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