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

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

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

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

To find the value of \( x \) that maximizes the profit, we can use the formula for the vertex of a parabola, given by \( x = -\frac{b}{2a} \).

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

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

Thus, the amount that will be directed toward marketing to achieve the maximum profit is \( 100 \) thousand dollars.

Answer: $100