Solve the following Linear Programming Problems graphically:
Maximise $Z = 3 x + 4 y$
subject to the constraints : $x + y \leq 4, x \geq 0, y \geq 0$

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Solution

Given objective function is $Z = 3 x + 4 y$

We have to maximize Z on given constraints
$x + y \leq 4$
$x \geq 0, y \geq 0$

After plotting all the constraints we get the common region (Feasible region) as shown in the image.

There are three corner points $(0, 4), (0, 0) a n d (4, 0)$

Now, at corner points value of Z are as follows :

Corner points Value of $Z = 3 x + 4 y$
(0,4) 16 (maximum)
(0,0) 0
(4,0) 12
So, value of Z is maximum at $(0, 4)$ and maximum value is 16.

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