Solve the following linear programming problem graphically.Minimi… - Vidyadip

Question

Solve the following linear programming problem graphically.Minimise $\text{z = 3x + 5y}$
subject to the constraints
$\text{x + 2y}\geq 10$
$\text{x + y}\geq 6$
$\text{3x + y}\geq 8$
$\text{x, y}\geq 0.$

✓

Answer

Vertices are A (10, 0), 2, 4 ), C(1, 5) & D (0, 8)$\text{Z = 3 x + 5y}$ is minimum
at B (2, 4) and the minimum Value is 26.
on Ploting $\text{(3x + 5y < 26)}$
since these it no common point with the feasible
region, Hence, $\text{x = 2, y = 4}$ gives minimum Z

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