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?

Answer 1

To find the amount of spending \( x \) on marketing that maximizes profit \( P \), we can use the formula for the vertex of a parabola given in the standard form \( P = ax^2 + bx + c \). The maximum or minimum value of a quadratic function represented by this form occurs at \( x = -\frac{b}{2a} \).

In your equation, \( P = -5x^2 + 1000x + 5000 \):

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

Now, we can calculate the vertex:

\[ x = -\frac{b}{2a} = -\frac{1000}{2(-5)} = -\frac{1000}{-10} = 100 \]

Thus, the amount to spend on marketing to achieve maximum profit is \( x = 100 \) thousand dollars.

So, the company should direct $100,000 toward marketing.

Answer 2

Wrong