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(B) To find the graphical solution set,we analyze the given system of inequations: $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,$y \g

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Fig. $2$

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(B) To find the graphical solution set,we analyze the given system of inequations: $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,$y \geq 0$.$1$. For $x+y \geq 1$: The line passes through $(1, 0)$ and $(0, 1)$. The region is away from the origin.$2$. For $7x+9y \leq 63$: The line passes through $(9, 0)$ and $(0, 7)$. The region is towards the origin.$3$. For $x \leq 6$ and $y \leq 5$: These represent the region bounded by the lines $x=6$ and $y=5$ in the first quadrant.$4$. The intersection of all these regions gives the feasible region. By plotting these lines,we observe that the region is bounded by the vertices $(0, 1), (0, 7), (2.57, 5), (6, 5), (6, 2.33)$ and $(1, 0)$.Comparing this with the provided figures,the correct graphical representation is Fig. $2$.

The graphical solution set of the system of inequations $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,$y \geq 0$ is represented by:

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