The corner points of the feasible region determined by
x + y ≤ 8, 2x + y ≥ 8, x ≥ 0, y ≥ 0
are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → a = 2b
Points A(0, 8) and B(4, 0) form the line segment AB.
Slope of AB = (0 − 8) / (4 − 0) = −8/4 = −2
For the objective function Z=ax+by
Its lines are of the form ax+by=k whose slope is −a/b.
For maximum value to lie along AB, the objective line must be parallel to AB, so:
−a/b = −2
⇒ a/b = 2
⇒ a = 2b
The correct answer is Option (2) → a = 2b