Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints $x + y ≤ 60,5x + y ≤ 100,x,y≥0$. If the maximum value of $Z$ occurs at $x=α$ and $y = β$, then the value of $α + β$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60
Feasible corner points: solve intersections of constraints and axes.
Intersection of $x+y=60$ and $5x+y=100$: subtract to get $4x=40\Rightarrow x=10,\;y=50$.
Other feasible vertices: $(0,0),\;(0,60),\;(20,0)$.
Evaluate $Z=50x+15y$ at vertices:
$Z(0,0)=0$
$Z(0,60)=15\cdot60=900$
$Z(20,0)=50\cdot20=1000$
$Z(10,50)=50\cdot10+15\cdot50=500+750=1250$
Maximum occurs at $(\alpha,\beta)=(10,50)$, hence $\alpha+\beta=60$. Answer: 60.