Question

Solve the following Linear Programming Problem by the method of graph:
Maximize
Z = 3x1 + 4x2
such that
x1 - x2 S-1
and
X1, X2 = 0​

Answer 1

Answer:

Solve the following Linear Programming Problem by the method of graph:

Maximize

Z = 3x1 + 4x2

such that

x1 - x2 S-1

and

X1, X2 = 0

Answer 2

$corresponding \: equation$

⬇⬇

$x1 - x2 \leqslant - 1➡x1 - x2 = - 1$

$Graph \: [Take \: x \: 1 \: on \: the \: x-axis \: and \: x \: 2 \: on \: the \: y-axis.]</p><p>$

$(i) x1 - x2 = - 1 for x2 = x1 + 1$

$if \: x1 = 0 \: \: \: - 1 \\ \\ then \: x2 = 1 \: \: \: 0 \: \: \: 1$

$Draw \: a \: line \: i \: joining \: the \: points A(0, 1) \: and \: B(-10).</p><p>$

$Substituting \: x1 - x2 \leqslant - 1, x1 = 0 \: in \: the \: inequality \: x2 = 0 \leqslant 0 - 0 \leqslant - 0 \: is \: false, \: so \: the \: origin \: will \: not \: be \: in \: the \: region \: satisfying \: this \: inequality.$

$(ii) x 1 \geqslant 0.x2 \geqslant 0 \: represent \: the \: first \: term. The \: required \: graph \: is \: as \: follows</p><p></p><p> \: It \: is \: clear \: that \: the \: potential \: area (shaded part) \: is \: infinite.$

The objective function at point A will have man Z = 3 × 0 + 4 × 1 = 4, since there are many points in the infinitely possible region at which the objective function Z has a value greater than 4, that is, the maximum value of Z is at infinity. Therefore, this Linear Processing Problem (LPP) has an infinitely possible solution.