Question 1186827
Here's how to solve this problem:

**1. Define the variables:**

*   p = price per tablet (dollars)
*   x = quantity of tablets (millions)

**2. Given information:**

*   Demand function: p = 200 - 16x²
*   Cost per tablet: $50
*   Profit: $125 million when x = 2.5 million

**3. Find the profit function:**

*   Revenue = p * x = (200 - 16x²) * x = 200x - 16x³
*   Cost = 50 * x
*   Profit = Revenue - Cost = (200x - 16x³) - 50x = 150x - 16x³

**4. Set up the equation to solve for x:**

We know the profit was $125 million when x = 2.5 million. We want to find the other value of x that gives the same profit.

125 = 150x - 16x³

**5. Solve for x:**

16x³ - 150x + 125 = 0

This is a cubic equation. We already know one root: x = 2.5. We can use this information to factor the equation or use numerical methods (like a calculator or software) to find the other root(s).

*One way to proceed is to use polynomial division to divide the cubic by (x - 2.5). This will leave you with a quadratic equation which you can then solve using the quadratic formula.*

Solving the cubic equation (using a calculator or software is the most practical method), we find three roots: x ≈ -3.06, x = 2.5, and x ≈ 3.56.

**6. Interpret the results:**

*   x ≈ -3.06: This solution doesn't make sense in our context, as the quantity of tablets cannot be negative.
*   x = 2.5: This is the given quantity, which we already know yields a profit of $125 million.
*   x ≈ 3.56: This is the other solution we're looking for.

**Answer:**

The company could sell approximately 3.56 million tablets to make the same amount of profit ($125 million).