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(B) Let $x$ and $y$ denote the quantity of copper and brass in grams,respectively.The objective function to minimize is the cost: $z = 8x + 5y$.The co

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₹ $31$

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(B) Let $x$ and $y$ denote the quantity of copper and brass in grams,respectively.The objective function to minimize is the cost: $z = 8x + 5y$.The constraints based on the problem are:$1) \ x + y \geq 5$ (Total weight at least $5 	ext{ gms}$)$2) \ x \geq 2$ (Minimum $2 	ext{ gms}$ of copper)$3) \ y \leq 4$ (Maximum $4 	ext{ gms}$ of brass)$4) \ x \geq 0, y \geq 0$ (Non-negativity constraints)The feasible region is determined by these inequalities. The corner points of the feasible region are found by the intersection of the boundary lines:- Point $A$: Intersection of $x = 2$ and $y = 4$,so $A = (2, 4)$.- Point $B$: Intersection of $x = 2$ and $x + y = 5$,so $B = (2, 3)$.- Point $C$: Intersection of $x + y = 5$ and $y = 0$,so $C = (5, 0)$.Now,evaluate the objective function $z = 8x + 5y$ at these corner points:- At $A(2, 4): z = 8(2) + 5(4) = 16 + 20 = 36$.- At $B(2, 3): z = 8(2) + 5(3) = 16 + 15 = 31$.- At $C(5, 0): z = 8(5) + 5(0) = 40 + 0 = 40$.The minimum value of $z$ is $31$.Therefore,the minimum cost is $₹ 31$.

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