A manufacturing company produces two items, A and B. Each toy should be processed by two machines, I and II. Machine I can be operated for maximum 10 hours 40 minutes. It takes 20 minutes for an item A and 15 minutes for B. Machine II can be operated for a total time at 8 hours 20 minutes. It takes 5 minutes for an item $A$ and 8 minutes for $B$. 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 number of items $A$ and $y$ is the number of item $B$ ) is _____

• A

  $\begin{aligned} & \text { Maximize } \mathrm{z}=25 x+18 \mathrm{y} \\ & \text { subject to } 20 x+15 y \leqslant 640 \\ & \qquad \begin{array}{r} 5 x+8 y \geqslant 500 \\ x, y \geqslant 0 \end{array} \end{aligned}$
• Correct answer
  B

  $\begin{array}{r}\text { Maximize } \mathrm{z}=25 x+18 \mathrm{y} \\ \text { subject to } 20 x+15 y \leqslant 640 \\ \qquad 5 x+8 y \leqslant 500 \\ \qquad x, y \geqslant 0\end{array}$
• C

  $\begin{aligned} & \text { Maximize } \mathrm{z}=25 x+18 \mathrm{y} \\ & \text { subject to } 20 x+5 y \leqslant 8 \\ & \qquad 5 x+8 y \leqslant 10 \\ & x, y \geqslant 0\end{aligned}$
• D

  $\begin{array}{r}\text { Maximize } \mathrm{z}=25 x+18 \mathrm{y} \\ \text { subject to } 4 x+3 y \leqslant 128 \\ \qquad \begin{array}{r}5 x+8 y \geqslant 500 \\ x, y \geqslant 0\end{array}\end{array}$

Hence, the correct answer is option: 'B'.