The linear programming problem :
minimise z = 3x + 2y
subject to the constraints
x + y ≥ 8,
3x + 5y ≤ 15, x ≥ 0, y ≥ 0
has
Answer & explanation
Correct answer: option 3
Z = 3x + 2y
constraints
x + y ≥ 8
3x + 5y ≤ 15
x, y ≥ 0 → solution lies in 1st quadrant
Solving for first
x + y = 8
| x | 8 | 0 |
| y | 0 | 8 |
3x + 5y = 15
| x | 5 | 0 |
| y | 0 | 3 |
Checking for point O(0, 0)
for: x + y ≥ 8
⇒ 0 ≥ 8 (false)
solution lies to side of x + y = 8 not containing O(0, 0)
for: 3x + 5y ≤ 15
⇒ 0 ≤ 15
solution lies to side of 3x + 5y = 15 containing O(0, 0)
⇒ No feasible region