Question

Consider the graph of constraints stated as linear inequalities as below
$5x+y\le 100$...(i)
$x+y\le 60$...(ii)
$x\ge 0$....(iii)
$y\ge 0$...(iv)

where, $x$ and $y$ are number of tables and chairs on which a furniture dealer wants to make his profit.
The shaded region in the graph is called

• A. feasible region
• B. critical region
• C. non-feasible region
• D. None of these

Answer 1

Answer: (A)

Constraints are
$5x+y\le 100$...(i)
$x+y\le 60$...(ii)
$x\ge 0$....(iii)
$y\ge 0$...(iv)

The graph of this system (shaded region) consists of the points common to all half planes determined by the inequalities (i) to (iv). Each point in this region represents a feasible choice open to the dealer for investing in tables and chairs. The region, therefore, is called the feasible region for the problem.