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)
$
Remaining Attempts : 3
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Answer 1

To determine the amount spent on marketing (x) that will achieve the maximum profit (P) for the given profit function \( P = -5x^2 + 1000x + 5000 \), we can find the vertex of the parabola represented by this quadratic equation.

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

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

Here, \( a = -5 \) and \( b = 1000 \).

Substituting these values into the formula gives:

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

Thus, the amount spent on marketing to achieve the maximum profit is $100,000 (since x is in thousands of dollars).