MHTCET 16 May 2024 Shift 1 Paper

Concept:In linear programming, the maximum value of $Z$ occurs at one of the corner points of the feasible region.Explanation:The constraints are $2x \geq 4 \Rightarrow x \geq 2$, $y \leq 3$, $x+y \leq 8$, and $x, y \geq 0$.The feasible region lies in the first quadrant, to the right of $x=2$, below $y=3$, and below $x+y=8$.The corner points of the feasible region are $A(2,0)$, $B(8,0)$, $C(5,3)$, and $D(2,3)$.Evaluate $Z = 100x + 70y$ at each corner point:At $A(2,0)$: $Z = 100(2) + 70(0) = 200$At $B(8,0)$: $Z = 100(8) + 70(0) = 800$At $C(5,3)$: $Z = 100(5) + 70(3) = 500 + 210 = 710$At $D(2,3)$: $Z = 100(2) + 70(3) = 200 + 210 = 410$The highest value is $800$, obtained at $B(8,0)$.Answer:Maximum value of $Z$ is $800$, i.e., option A.