Question

mario has a business selling muffins. let x be the price of a muffin. then, the profit p for marios business is given by p(x) = -100x² + 350x - 150. choose the inequality that shows the business will make a positive profit. options: 0 ≥ -100x² + 350x - 150; 0 ≤ -100x² + 350x - 150; 0 > -100x² + 350x - 150; 0 < -100x² + 350x - 150.

Explanation:

Step1: Understand Profit Definition

Profit \( P(x) \) is positive when \( P(x) > 0 \). Here, \( P(x)= -100x^2 + 350x - 150 \), so positive profit means \( 0 < -100x^2 + 350x - 150 \).

Step2: Analyze Inequality Options

• \( 0 \geq -100x^2 + 350x - 150 \): Includes non - positive profit (profit ≤ 0), not what we want.
• \( 0 \leq -100x^2 + 350x - 150 \): Also includes non - positive profit (profit ≥ 0 but we need profit > 0), incorrect.
• \( 0 > -100x^2 + 350x - 150 \): This would mean profit is negative, opposite of what we need.
• \( 0 < -100x^2 + 350x - 150 \): This represents profit \( P(x)>0 \), which is positive profit.

Answer:

\( 0 < -100x^2 + 350x - 150 \) (the last option: \( 0 < -100x^2 + 350x - 150 \))