Question

The profit P (in millions of dollars) for a game company can be modeled by P =−x³ + 3x² + 3, where x is the

number (in millions) of copies of a new game produced. The company now produces 1 million copies of the new
game and makes a profit of $5 million, but it would like to increase production. What greater number of copies could
the company produce and still make the same profit?

Answer 1

To make the same profit, the company could produce either 2 million copies or 1 million copy.

Step-by-step explanation:

To find the maximum number of copies the company could produce and still make the same profit, we need to set the profit equation equal to the current profit amount and solve for x:

P = -x³ + 3x² + 3

5 = -x³ + 3x² + 3

Next, we simplify the equation:

x³ - 3x² + 2 = 0

By factoring, we can find the solutions:

(x - 2)(x - 1)² = 0

So, the company could produce either 2 million copies or 1 million copy to make the same profit.