MHTCET 15 May 2024 Shift 1 Paper

Concept:The feasible region is the set of points satisfying all given inequalities simultaneously.Explanation:For $2x+3y \leq 18$, the origin satisfies $0 \leq 18$, so the region lies on the origin side of this line.For $x+y \geq 10$, the origin does not satisfy $0 \geq 10$, so the region lies on the non-origin side.Now, on the line $x+y=10$, express $2x+3y=2x+3(10-x)=30-x$.For $0 \leq x \leq 10$, the minimum value of $30-x$ is $20$, which is greater than $18$.Hence, no point in the first quadrant can satisfy both $2x+3y \leq 18$ and $x+y \geq 10$.Answer:The feasible region is empty, so it is a null set.Correct option: D. null set.