Solve the following L.P.P. graphically: Miximise Z = 4x + y Subec… - Vidyadip

Question

Solve the following L.P.P. graphically:
$\text{Miximise}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{ }\text{ }\text{ }\text{Z} = 4x + \text{y}\\ \text{Subect to following constraints} \text{ }\text{ }\text{ }\text{ }\text{ }x + \text{y} \leq 50\\ \ \ \ \ \ \ \ \ \ \ \ \text{}\text{} \text{ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x + \text{y} \leq 90\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \ \geq 10\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x, \text{y} \geq 0$

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Answer

$Z|_{A(10, 0)} = 40$
$Z|_{B(30, 0)} = 120$
$Z|_{C(20, 30)} = 110$
$Z|_{D(10, 40}) = 80$
Minimum value of $Z = 120$ at $(30, 0)$

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