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A product made in two factories, $P$ and $Q$, is transported to two destinations, $R$ and $S$. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:

$$\begin{array}{|l|l|l|} \hline \text{Factory/Destinations} & R & S \\ \hline P & 10 & 7 \\ \hline Q & 3 & 4 \\ \hline \end{array}$$

Factory $P$ produces $7$ units and factory $Q$ produces $9$ units of the product. Each destination requires $8$ units. If the North-West corner method provides the total transportation cost as $X$ (in Rupees) and the optimized (the minimum) total transportation cost is $Y$ (in Rupees), then $(X-Y)$, in Rupees, is

  1. $0$
  2. $15$
  3. $35$
  4. $105$
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