Consider the following L.P.P minimize $z = x-7y+190$ subject to $x + y ≤8,x + y ≥ 4,x ≤ 5,y ≤ 5$ and $x, y≥0$. Then which of the following is/are true?

(A) It's feasible region is unbounded
(B) It's feasible region is bounded
(C) It's feasible region has 5 corner points
(D) It's feasible region has 6 corner points

Choose the correct answer from the options given below:

(B) and (D) only

The correct answer is Option (4) → (B) and (D) only

(A) It's feasible region is unbounded (False)
(B) It's feasible region is bounded (True)
(C) It's feasible region has 5 corner points (False)
(D) It's feasible region has 6 corner points (True)

Given LPP: Minimize $z = x - 7y + 190$

Subject to constraints:

• $x + y \leq 8$
• $x + y \geq 4$
• $x \leq 5$
• $y \leq 5$
• $x \geq 0,\ y \geq 0$

Step: Analyze feasible region

The region is bounded by:

• Two lines: $x + y = 8$ and $x + y = 4$
• Two vertical/horizontal lines: $x = 5$ and $y = 5$
• Coordinate axes: $x = 0$ and $y = 0$

All constraints form a closed polygon in the first quadrant → Bounded region.

Total: 6 corner points