The profit of a company is represented by P=-5x^2+1000x+5000 where P is profit and x is amount spent on marketing (in thousands of dollars). How much spending in thousands of dollars will be directed toward marketing to achieve maximum profit?

To find the amount spent on marketing that will achieve the maximum profit, we can analyze the quadratic profit function:

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

This is a quadratic function in the standard form \(P = ax^2 + bx + c\), where:

• \(a = -5\)
• \(b = 1000\)
• \(c = 5000\)

Since \(a < 0\), this parabola opens downwards, which means it has a maximum point.

The \(x\)-coordinate of the vertex of a parabola given by the function \(P = ax^2 + bx + c\) can be found using the formula:

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

Substituting in the values of \(a\) and \(b\):

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

Thus, the maximum profit occurs when \(x = 100\).

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

\[ \boxed{100} \text{ (in thousands of dollars)} \]