$A$ manufacturing company produces two items,$A$ and $B$. Each item must be processed by two machines,$I$ and $II$. Machine $I$ can be operated for a maximum of $10$ hours $40$ minutes ($640$ minutes). It takes $20$ minutes for an item $A$ and $15$ minutes for an item $B$. Machine $II$ can be operated for a maximum of $8$ hours $20$ minutes ($500$ minutes). It takes $5$ minutes for an item $A$ and $8$ minutes for an item $B$. The profit per item of $A$ is ₹ $25$ and per item of $B$ is ₹ $18$. The formulation of an $L.P.P.$ to maximize the profit (where $x$ is the number of items $A$ and $y$ is the number of items $B$) is . . . . . . .

• A
  Maximize $z=25x+18y$ subject to $20x+15y \leqslant 640, 5x+8y \geqslant 500, x, y \geqslant 0$
• B
  Maximize $z=25x+18y$ subject to $20x+15y \leqslant 640, 5x+8y \leqslant 500, x, y \geqslant 0$
• C
  Maximize $z=25x+18y$ subject to $20x+5y \leqslant 8, 5x+8y \leqslant 10, x, y \geqslant 0$
• D
  Maximize $z=25x+18y$ subject to $4x+3y \leqslant 128, 5x+8y \geqslant 500, x, y \geqslant 0$