Solve the following L.P.P. graphically: Minimise Z = 5x + 10y to … - Vidyadip

Question

Solve the following L.P.P. graphically:
$\text{Minimise} \text{ }\text{ }\text{ }\text{Z} = 5x + 10\text{y}\\\text{Subect to} \text{ }\text{ }\text{ }\text{ }\text{ }x + \text{2y} \leq 120\\\text{Constraints} \text{ }x + \text{y} \geq 60\\\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }x - \text{2y} \geq 0\\\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{and}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }x, \text{y} \geq 0$

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Answer

$Z = 5x + 10y$
$Z|_{A(60, 0)} = 300$
$Z|_{B(120, 0)} = 600$
$Z|_{C(60, 30)} = 60$
$Z|_{D(40, 20}) = 400$
Minimum value of $Z = 300$ at $x = 60, y = 0$

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