8
algebra

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

A

Below 20f+10d=48020f + 10d = 480, right of f=5f=5, first quadrant

B

Above 20f+10d=48020f + 10d = 480, right of f=5f=5, first quadrant

C

Below 20f+10d=48020f + 10d = 480, left of f=5f=5, first quadrant

D

Below 20f+10d=48020f + 10d = 480, right of d=5d=5, first quadrant

Correct Answer: A

Choice A is the correct answer. Translate to geometry.

  1. Time: 20f+10d≤48020f + 10d \leq 480. "Less than" means below the line.
  2. Quantity: f≥5f \geq 5. "Greater than" means to the right of vertical line f=5f=5.
  3. Quadrant: f,d≥0f,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≤5f \leq 5). Choice D is incorrect because it uses the wrong variable for the minimum quantity.

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Linear Functions Set 78