the profit (in thousands of dollars) of a company is represented as p = -5x² + 1,000x + 5,000, where p…

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)

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

Explanation:

Step1: Identify the quadratic - function form

The profit function is $P = - 5x^{2}+1000x + 5000$, which is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-5$, $b = 1000$, and $c = 5000$.

Step2: Use the formula for the x - coordinate of the vertex

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the value of x for the maximum or minimum of the function) is $x=-\frac{b}{2a}$. Substitute $a=-5$ and $b = 1000$ into the formula: $x=-\frac{1000}{2\times(-5)}$.

Step3: Calculate the value of x

First, calculate the denominator: $2\times(-5)=-10$. Then, $x=\frac{-1000}{-10}=100$.

Answer:

100