The corner points of the bounded feasible reg | vedclass

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(B) To find the maximum and minimum values of the objective function $Z = 3x - y$,we evaluate $Z$ at each corner point of the feasible region:						Co

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$(i) (0,7), (ii) (6,0), (iii) 18, (iv) -7$

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(B) To find the maximum and minimum values of the objective function $Z = 3x - y$,we evaluate $Z$ at each corner point of the feasible region:						Corner Point $(x, y)$			Value of $Z = 3x - y$							$(0, 1)$			$Z = 3(0) - 1 = -1$							$(0, 7)$			$Z = 3(0) - 7 = -7$ (Minimum)							$(2, 7)$			$Z = 3(2) - 7 = -1$							$(6, 3)$			$Z = 3(6) - 3 = 15$							$(6, 0)$			$Z = 3(6) - 0 = 18$ (Maximum)							$(1, 0)$			$Z = 3(1) - 0 = 3$			From the table,we observe:$(i)$ $Z$ is minimum at $(0, 7)$.$(ii)$ $Z$ is maximum at $(6, 0)$.$(iii)$ The maximum value of $Z$ is $18$.$(iv)$ The minimum value of $Z$ is $-7$.Thus,the correct option is $B$.

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The corner points of the bounded feasible region are $(0,1), (0,7), (2,7), (6,3), (6,0), (1,0)$. For the objective function $Z = 3x - y$:$(i)$ At which point is $Z$ minimum?$(ii)$ At which point is $Z$ maximum?$(iii)$ The maximum value of $Z$ is $\ldots$$(iv)$ The minimum value of $Z$ is $\ldots$