Maximum Z -3 x -4 y- subject to the constraints x - y - 1- x - 0- y - 0

Maximise Z =3x+4y, Subject to the constraints x+y ≤ 1, x ≤ 0, y ≤ 0 The shaded region shown in the figure as OAB is bounded and the coordinates of corner points ...

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Standard XII

Mathematics

Linear Programming Problems

Maximum Z =3 ...

Question

Maximum Z=3x +4y, subject to the constraints $x + y \leq 1, x \leq 0, y \leq 0$ .

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Solution

Maximise Z =3x+4y, Subject to the constraints
$x + y \leq 1, x \leq 0, y \leq 0$
The shaded region shown in the figure as OAB is bounded and the coordinates of corner points O, A and B are(0,0) and (0,1), respectively.

$\begin{matrix} Corner points & Corresponding value of Z (0, 0) & 0 (1, 0) & 3 (0, 1) & 4 \leftarrow Maximum \end{matrix}$
Hence, the maximum value of Z is 4 at (0,1).

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Maximum Z=3x +4y, subject to the constraints x+y≤1,x≤0,y≤0.

Maximum Z=3x +4y, subject to the constraints $x + y \leq 1, x \leq 0, y \leq 0$ .