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 can use the formula for the vertex of a quadratic function. The general form of a quadratic function is \( P = ax^2 + bx + c \). In your case, the function is given as:

\[ P = -5x^2 + 1,000x + 5,000 \]

Here, \( a = -5 \), \( b = 1,000 \), and \( c = 5,000 \).

The x-coordinate of the vertex (which gives the maximum profit for a downward-opening parabola) can be found using the formula:

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

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

\[ x = -\frac{1,000}{2 \times -5} = -\frac{1,000}{-10} = 100 \]

So, the amount that should be spent on marketing to achieve maximum profit is 100 thousand dollars.