The profit (in thousands of dollars) of a company is represented as P=−5x2+1,000x+5,000

Question

, 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:

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

The vertex \( x \) of a quadratic function in the form \( ax^2 + bx + c \) can be calculated using the formula:

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

In this equation:

• \( a = -5 \)
• \( b = 1000 \)

Substituting the values of \( a \) and \( b \) into the vertex formula:

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

Thus, the amount that should be spent on marketing to achieve the maximum profit is:

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