Minimum value of Z - x -5 y -20 under the given conditions - x - y - 0- - x -2 y - 2- x - 3- y - 4- x - y - 0 -isA- 4 - B- 8- C- 1- D- 6 -

The correct option is A 4First draw the feasible region nbsp; x y=0 x+2y=2 x=3 y=4 From the above figure, the corner points of the feasible region are n ...

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Standard XII

Mathematics

Graphical Method of Solving Linear Programming Problems

Minimum value...

Question

Minimum value of $Z = x - 5 y + 20$ under the given conditions
$x - y \geq 0 - x + 2 y \geq 2 x \geq 3, y \leq 4 x, y \geq 0$
is

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Solution

The correct option is A $4$
First draw the feasible region
$x - y = 0 - x + 2 y = 2 x = 3 y = 4$

From the above figure, the corner points of the feasible region are

Corner point Objective function $Z = x - 5 y + 20$

$A (3, 3)$ $8$

$B (3, 2.5)$ $10.5$

$C (6, 4)$ $6$

$D (4, 4)$ $4 \to$ minimum

$∴ Z_{minimum} = 4$ at $D (4, 4)$

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Corner point	Objective function $Z = x - 5 y + 20$
$A (3, 3)$	$8$
$B (3, 2.5)$	$10.5$
$C (6, 4)$	$6$
$D (4, 4)$	$4 \to$ minimum

Minimum value of Z=x−5y+20 under the given conditions x−y≥0−x+2y≥2x≥3,y≤4x,y≥0 is

The correct option is A 4First draw the feasible region x−y=0−x+2y=2x=3y=4 From the above figure, the corner points of the feasible region are Corner point Objective function Z=x−5y+20 A(3,3) 8 B(3,2.5) 10.5 C(6,4) 6 D(4,4) 4→ minimum ∴Zminimum=4 at D(4,4)

Minimum value of $Z = x - 5 y + 20$ under the given conditions
$x - y \geq 0 - x + 2 y \geq 2 x \geq 3, y \leq 4 x, y \geq 0$
is