Ashok bought tables and chairs for a marriage hall. The cost of a table is $₹2500$ and a chair is $₹500$. He has a budget of $₹60000$ and space for at most $60$ items. If the profit is $₹75$ per table and $₹25$ per chair, find the maximum profit.

Let $x$ be the number of chairs and $y$ be the number of tables.Objective function: Maximize $Z=25x+75y$ Constraints:$500x+2500y\le 60000⟹x+5y\le 120$$x+y\le 60$$x,y\ge 0$ Corner points of the feasible region:Intersection of $x+5y=120$ and $x+y=60$:Subtracting: $4y=60⟹y=15$. Then $x=45$. Point: $(45,15)$.X-intercepts: $(60,0)$ for $x+y=60$ and $(120,0)$ for $x+5y=120$. Feasible is $(60,0)$.Y-intercepts: $(0,60)$ for $x+y=60$ and $(0,24)$ for $x+5y=120$. Feasible is $(0,24)$.Origin: $(0,0)$.Evaluate $Z$ at corner points:$Z(0,0)=0$$Z(60,0)=25(60)=1500$$Z(0,24)=75(24)=1800$$Z(45,15)=25(45)+75(15)=1125+1125=2250$ Maximum profit is $₹2250$.