Question

The area of the feasible region for the following constraints $3y+x\ge 3$,$x\ge 0$ and $y\ge 0$will be

• A. bounded
• B. unbounded
• C. convex
• D. concave

Answer 1

The correct option is B

unbounded

Explanation for Correct Answer:

Given constraints are $3y+x\ge 3$,$x\ge 0$ and $y\ge 0$

$3y+x\ge 3\to \left(i\right)$

Put $x=0$ we get,

$$\begin{gathered} 3y+0=3 \\ \Rightarrow 3y=3 \\ \Rightarrow y=1 \end{gathered}$$

Hence the point is $\left(0,1\right)$.

Put $y=0$, We get,

$$\begin{gathered} 3\left(0\right)+x=3 \\ \Rightarrow x=3 \end{gathered}$$

Hence the point is $\left(3,0\right)$.

Now put the point of origin $(0,0)$ in the given equation and see if it satisfies the condition.

$$\begin{gathered} 3\left(0\right)+0\ge 3 \\ \Rightarrow 0\ge 3 \end{gathered}$$

which is not true.

Hence, the given line only covers the area towards its upper side in the first quadrant.

Therefore, the area is unbounded.

Hence, option (B) is the correct .