Maximise Z=x+2ysubject to the constraintsx+2y≥1002x−y≤02x+y≤200x,y≥0Solve the above LPP graphically.

Minimize & Maximize z=x+2ySubject to,x+2y≥1002x−y≤02x+y≤200x,y≥0x+2y∣≥100x0100y5002x−y≤0 x050y01002x+y≤200 y1000x0200∴Z=400 is maximum at (0,200)Also,Z is minimum at two points (0,50) & (20,40)∴Z=100 is minimum at all points joining (0,50) & (20,40)

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Maximise $Z = x + 2 y$
subject to the constraints
$\begin{aligned} x + 2 y \geq 100 \\ 2 x - y \leq 0 \\ 2 x + y \leq 200 \\ x, y \geq 0 \end{aligned}$
Solve the above LPP graphically.

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Detailed Solution

Minimize & Maximize $z = x + 2 y$
Subject to,
$\begin{array}{l} x + 2 y \geq 100 \\ 2 x - y \leq 0 \\ 2 x + y \leq 200 \\ x, y \geq 0 \end{array}$
$x + 2 y ∣\geq 100$

x	0	100
y	50	0

$2 x - y \leq 0$

x	0	50
y	0	100

$2 x + y \leq 200$

y	100	0
x	0	200

∴Z=400 is maximum at (0,200)
Also,
Z is minimum at two points (0,50) & (20,40)
∴Z=100 is minimum at all points joining (0,50) & (20,40)
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