The feasible region is a quadrilateral lying entirely in the first quadrant and…

MATHEMATICS · Single correct · CBSE · Mathematics · Linear Inequalities · Linear Inequalities

Problem

The feasible region is a quadrilateral lying entirely in the first quadrant and bounded by the xx-axis, the yy-axis, the solid line 2x+y=102x+y=10, and the dashed line x+y=6x+y=6. The region lies below both slant lines. Which system of inequalities correctly describes this feasible region? (a) {x≥0,y≥0,2x+y≤10,x+y≤6\begin{cases}x\ge0,\\ y\ge0,\\ 2x+y\le10,\\ x+y\le6\end{cases} (b) {x≥0,y≥0,2x+y≤10,x+y<6\begin{cases}x\ge0,\\ y\ge0,\\ 2x+y\le10,\\ x+y<6\end{cases} (c) {x≥0,y≥0,2x+y≥10,x+y<6\begin{cases}x\ge0,\\ y\ge0,\\ 2x+y\ge10,\\ x+y<6\end{cases} (d) {x≥0,y≥0,2x+y≤10,x+y>6\begin{cases}x\ge0,\\ y\ge0,\\ 2x+y\le10,\\ x+y>6\end{cases}

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