The feasible region corresponding to an LPP represented by the constraints x ≥7, y ≥ 4,x + 2y  ≥ 8 is

The correct option is: Unbounded and feasible.

To determine the properties of the feasible region, we analyze the given system of linear inequalities (constraints):
$x\ge 7$
$y\ge 4$
$x+2y\ge 8$

Step 1: Check for Feasibility
A feasible region consists of all points that satisfy all constraints simultaneously. Let us verify if such points exist.
Consider the point where both boundary lines of the first two constraints meet, i.e.,
$x=7$
and
$y=4$
This point clearly satisfies:
$x\ge 7$
(since
$7\ge 7$
is true) and
$y\ge 4$
(since
$4\ge 4$
is true).

Now, we substitute these coordinates into the third constraint:
$x+2y=7+2\left(4\right)=7+8=15$
Since
$15\ge 8$
is true, the point (7, 4) satisfies all three inequalities. Thus, the system is consistent, and the feasible region exists (is feasible).

Step 2: Check if the Region is Bounded or Unbounded
A feasible region is bounded if it can be enclosed within a circle of a finite radius. Otherwise, it is unbounded.
The constraints
$x\ge 7$
and
$y\ge 4$
indicate that the values of
$x$
and
$y$
must be at least 7 and 4, respectively. However, there is no upper limit on either
$x$
or
$y$
. They can grow infinitely large towards positive infinity.
For instance, any point such as (100, 100), (1000, 1000), or generally any point where
$x\ge 7$
and
$y\ge 4$
will satisfy all the constraints. Since the region extends infinitely in the positive directions of the coordinate axes, it cannot be enclosed. Hence, the feasible region is unbounded.

Conclusion:
Since the feasible region contains valid points and extends infinitely, it is both unbounded and feasible.