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Q.
Maximum value of $12 x+3 y$ subject to constraints $x \geq 0$, $y \geq 0, x+y \leq 5$ and $3 x+y \leq 9$ is
Linear Programming
Solution:
Given, constraints are $x \geq 0, y \geq 0, x+y \leq 5$
and $3 x +y \leq 9$ and $z=12 x+3 y$
Here, feasible region of $OABC$
At point $O (0,0),\, z =12(0)+ 3(0)= 0$
At point $A (3,0),\, z =12(3)+ 3(0)= 36$
At point $B (2,3),\, z =12(2)+ 3(3)= 33$
At point $C(0,5),\, z =12(0)+ 3(5)= 15$
Hence, maximum value is 36.
