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:
Answer & explanation
Correct answer: option 4
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
