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  4. The maximum value of z = 9x + 13y subject to 2x + 3y le 18, 2x + y le 10, x ge 0, y ge 0 is

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Q. The maximum value of $ z = 9x + 13y $ subject to $ 2x + 3y \le 18, 2x + y \le 10, x \ge 0, y \ge 0 $ is

MHT CETMHT CET 2009

Solution:

The feasible region is $OABC$.
image
At $\,\,\,\, O(0,0), z=0$
At $\,\,\,\,A(5,0), z=45$
At $\,\,\,\, B(3,4), z=27+52=79$
At $\,\,\,\, C(0,6), z=78$
$\therefore $ Maximum value of $z$ is $79$