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Graphical Method of Solving Linear Programming Problems

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Question

Solve the following Linear Programming Problems graphically:
Minimise $Z = - 3 x + 4 y$
subject to $x + 2 y \leq 8, 3 x + 2 y \leq 12, x \geq 0, y \geq 0$ .

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Solution

Corner points Value of Z
$(0, 4)$ 16
$(2, 3)$ 6
$(4, 0)$ -12

Hence $Z m i n = - 12$ is minimum at $(4, 0)$

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