GUJCET 2025 Math Paper

Concept:The maximum value of a linear objective function over a feasible region occurs at one of its corner points.Explanation:The constraints are $3x+5y \leq 15$, $x \geq 0$, and $y \geq 0$.Find the intercepts of $3x+5y=15$.If $x=0$, then $5y=15 \Rightarrow y=3$, so the point is $(0,3)$.If $y=0$, then $3x=15 \Rightarrow x=5$, so the point is $(5,0)$.The feasible region has corner points $(0,0)$, $(5,0)$, and $(0,3)$.Evaluate $z=5x+3y$ at each corner point.At $(0,0)$: $z=5(0)+3(0)=0$.At $(5,0)$: $z=5(5)+3(0)=25$.At $(0,3)$: $z=5(0)+3(3)=9$.So, the maximum value is $25$.Answer:$\boxed{25}$