Question

Region represented by the in equation system $x+y\le 3,y\le 6$ and $x\ge 0,y\ge 0$ is:

• (A) Unbounded in first quadrant
• (B) Unbounded in first and second quadrant
• (C) Bounded in first quadrant
• (D) None of the these

Answer 1

The Correct Option is C

Explanation:
Given:$x+y\le 3,y\le 6$ and $x\ge 0,y\ge 0$Converting the given in equations into equations$x+y=3$.......(1)$y=6\dots \text{...(2) }$Reglon represented by $x+y\le 3$ :The line $x+y=3$ meets the coordinate axes are $\mathrm{A}(3,0)$ and $\mathrm{B}(0,3)$ respectively,$x+y=3$$\begin{array}{|lll|}\hline \mathrm{x}& 3& 0\\ \mathrm{y}& 0& 3\\ \hline\end{array}$$\mathrm{A}(3,0);\mathrm{B}(0,3)$Join points $A$ and $B$ to obtain the line.Clearly, $(0,0)$ satisfies the in equation $x+y\le 3$.So, the region containing the origin represent the solution set of the in equation.Reglon represented by $y\le 6$ :The line $y=6$ is parallel to $x$-axis and its every point will satisfy the in equation in first, quadrant, region containing the origin represents the solution set of this in equation.Reglon represented by $x\ge 0$ and $y\ge 0$ :Since every point in first quadrant satisfy the in equations, so the first quadrant is the solution set of these in equations.

The shaded region is the common region of in equations. This is feasible region of solution which is bounded and is in first quadrant.Hence, the correct option is (C).