Question

The region represented by the solution of system of inequalities $5x+4y\le 40,x\ge 2,y\ge 3$ is

• A. bounded
• B. unbounded
• C. Does not exist
• D. None of the above

Answer 1

Answer: (A)

We first draw the graph of the lines
$5x+4y=40,x=2\text{ and }y=3$
Then, we note that the inequality (i) represents shaded region below the line $5x+4y=40$ and inequality (ii) represents the shaded region right of line $x=2$ but inequality shaded region above the line $y=3$. Hence, shaded region (figure) including all the point on the lines are also the solution of the given system of the linear inequalities.
In many practical situations involving system of inequalities the variable $x$ and $y$ often represent quantities that cannot have negative values, for example, number of units produced, number of articles purchased, number of hours worked, etc. Clearly, in such cases, $x\ge 0,y\ge 0$ and the solution region lies only in the first quadrant.
Since, the region is enclosed, so it is bounded.