MHTCET 18 Apr 2026 Shift 2 Paper

Concept:For a linear programming problem, the maximum value of a linear objective function under linear constraints occurs at one of the corner points of the feasible region.Explanation:The objective function is $z=4x+y$.The feasible region is bounded by the constraints:$$x+y \leq 5,\quad 2x+y \leq 7,\quad 3x+2y \leq 11,\quad x \geq 0,\quad y \geq 0.$$Find the corner points by solving the boundary equations pairwise and checking feasibility.The feasible corner points are:$$(0,0),\quad \left(\frac{7}{2},0\right),\quad (3,1),\quad (1,4),\quad (0,5).$$Now evaluate $z=4x+y$ at each corner point.At $(0,0)$: $z=4(0)+0=0$.At $\left(\frac{7}{2},0\right)$: $z=4\left(\frac{7}{2}\right)+0=14$.At $(3,1)$: $z=4(3)+1=13$.At $(1,4)$: $z=4(1)+4=8$.At $(0,5)$: $z=4(0)+5=5$.The largest value is $14$, achieved at $\left(\frac{7}{2},0\right)$.Answer:The maximum value is $14$, so the correct option is D.