Linear Inequalities

Concept:Identify the inequalities that define the shaded region bounded by the lines $x=0$, $y=0$, $x+y=20$, and $2x+4y=85$.Explanation:The region OMNO has vertices at O(0,0), M on the x-axis, N at the intersection of the two lines, and back to O.The shaded region lies below both lines $x+y=20$ and $2x+4y=85$ because it includes the origin (0,0), which satisfies $0+0 \leq 20$ and $2(0)+4(0) \leq 85$.Hence the inequalities are $x+y \leq 20$, $2x+4y \leq 85$, and $x \geq 0$, $y \geq 0$.Answer:Option B.