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Graphical Method of Solving Linear Programming Problems

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Question

Solve the following L.P.P. graphically .Minimize $Z = 3 x + 5 y$ .S
Subject to constraints
$2 x + 3 y \geq 12$
$- x + y \leq 3$
$x \leq 4$
$y \geq 3$

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Solution

Corner points are $(4, 3), (4, 7), (\frac{3}{2}, 3) (\frac{3}{5}, \frac{18}{5}$
$(4, 3), Z = 3 x + 5 y = 12 + 15 = 27$
$(4, 7), z = 3 x + 5 y = 12 + 35 = 47$
$(\frac{3}{2}, 3), Z = 3 x + 5 y = \frac{9}{2} + 15 = \frac{39}{2} = 19.5$
$(\frac{3}{5}, \frac{18}{5}), Z = 3 x + 5 y = \frac{9}{5} + 18 = 19.8$
Z is minimum at $(\frac{3}{2}, 3)$

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