The profit (in thousands of dollars) of a company is represented as P=−5x^2+1,000x+5,000 , where P represents the 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?(1 point) $

Answer 1

To find the amount spent on marketing that will achieve the maximum profit, we need to determine the vertex of the quadratic function given by the profit formula:

\[ P = -5x^2 + 1000x + 5000 \]

In a quadratic equation of the form \( P = ax^2 + bx + c \), the x-coordinate of the vertex (which gives the maximum profit for a parabola that opens downwards) can be found using the formula:

\[ x = -\frac{b}{2a} \]

In this case, \( a = -5 \) and \( b = 1000 \). Plugging in these values:

\[ x = -\frac{1000}{2(-5)} = -\frac{1000}{-10} = 100 \]

Therefore, the amount spent on marketing to achieve the maximum profit is:

\[ \boxed{100} \text{ thousand dollars} \]