Solve the following Linear programming problems graphically :
Maximize $z = 3 x + 4 y$ subject to the constraints : $x + y \leq 4, x \geq 0, y \geq 0$

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Solution

$x + y \leq 4$

x

0

4

y

4

0

Corner points

Value of z=3x+4y

(0,4)

16

(4,0)

9

(0,0)

0

Hence, z is maximum at (0,4) and max value is $16$

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