Solve the following Linear Programming Problems graphically:
Maximise $Z = 3 x + 2 y$
subject to $x + 2 y \leq 10, 3 x + y \leq 15, x, y \geq 0$ .

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Solution

The inequalities $x, y \geq 0$ can be graphed.

By alternately putting x and y = 0 we can plot $x + 2 y = 10$ and $3 x + y = 15$

The inequalities can be graphed as shown.

We get polygon ABCD

We need to check value of Z at all 4 corner points.

$Z = 3 x + 2 y$ must be maximised.

$Z (0, 0) = 0; Z (5, 0) = 15; Z (4, 3) = 18; Z (0, 5) = 10$

Clearly Z is maximised at (4,3) subject to given constraints.

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