Part (g)should be Price for at least $12,112 in Revenue

Let's adjust part (g) for the price required to earn at least $12,112 in revenue.

### Part (g): Price for at least $12,112 in Revenue
Find the intersection of $ R $ and $ 12112 $:
\[ 12112 = -8p^2 + 800p \]
\[ -8p^2 + 800p - 12112 = 0 \]

Solve the quadratic equation:
\[ 8p^2 - 800p + 12112 = 0 \]
\[ p^2 - 100p + 1514 = 0 \]

Use the quadratic formula $ p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $:
\[ a = 1, \, b = -100, \, c = 1514 \]
\[ p = \frac{100 \pm \sqrt{10000 - 6056}}{2} \]
\[ p = \frac{100 \pm \sqrt{3944}}{2} \]
\[ p = \frac{100 \pm 62.79}{2} \]

So, we get two solutions for $ p $:
\[ p = \frac{100 + 62.79}{2} \approx 81.40 \]
\[ p = \frac{100 - 62.79}{2} \approx 18.60 \]

Therefore, to earn at least $12,112 in revenue, the company should charge a price between $18.60 and $81.40.

Would you like more details on any specific part of this solution?

Here are 5 questions you might ask:
1. Can you explain how to solve a quadratic equation using the quadratic formula in more detail?
2. How do you determine if a quadratic equation has real or complex roots?
3. What are the implications of the discriminant value in the quadratic formula?
4. Can you provide an example of graphing a quadratic function with these roots?
5. How does changing the revenue target affect the required price range?

**Tip:** When using the quadratic formula, ensure you accurately calculate the discriminant ($ b^2 - 4ac $) to determine the nature and number of roots.

Learn how to calculate the price range required to achieve at least $12,112 in revenue using the quadratic equation. This problem involves solving a quadratic equation to determine the pricing strategy for maximizing revenue. Suitable for high school level students.

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