Set 16: Linear Inequalities (Advanced)

Explanation

Answer: A

A store sells two types of lamps. Floor lamps ( $f$ ) take 20 mins to assemble, desk lamps ( $d$ ) take 10 mins. Total time: 8 hours (480 mins). They must sell at least 5 floor lamps. Which graph region represents this?

Below $20f + 10d = 480$ , right of $f=5$ , first quadrant

✓ Correct

Above $20f + 10d = 480$ , right of $f=5$ , first quadrant

Below $20f + 10d = 480$ , left of $f=5$ , first quadrant

Below $20f + 10d = 480$ , right of $d=5$ , first quadrant

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Translate to geometry. 1. Time: $20f + 10 d \leq 480$ . "Less than" means below the line. 2. Quantity: $f \geq 5$ . "Greater than" means to the right of vertical line $f=5$ . 3. Quadrant: $f,d \geq 0$ (First quadrant). Strategic Tip: Identify the boundary lines and shading direction for each constraint. Choice B is incorrect because it shades above (more time than available). Choice C is incorrect because it shades left ( $f \leq 5$ ). Choice D is incorrect because it uses the wrong variable for the minimum quantity.

Key Steps:

•

The correct answer is Below $20f + 10d = 480$ , right of $f=5$ , first quadrant

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

← Previous Next →

Start Practicing

Set 16: Linear Inequalities (Advanced)

Detailed Explanation

🎯 Keep Practicing!