Minimise Z -13 x -15 y subject to the contraints x - y - 7-2 x -3 y -6 - 0- x - 0 and y - 0

Minimise Z =13 x 15 y subject to the constraints x+y ≤ 7, 2x 3y+6 ≥ 0, x ≥ 0, y ≥ 0. Shaded region shown as OABC is bounded and coordinates of its corner point ...

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Standard XII

Mathematics

Definition of Function

Minimise Z =1...

Question

Minimise Z =13x -15 y subject to the contraints $x + y \leq 7, 2 x - 3 y + 6 \geq 0, x \geq 0$ and $y \geq 0$

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Solution

Minimise Z =13 x-15 y subject to the constraints $x + y \leq 7, 2 x - 3 y + 6 \geq 0, x \geq 0, y \geq 0$ .

Shaded region shown as OABC is bounded and coordinates of its corner points are (0,0), (7,0), (3,4) and (0,2), respectively.

$\begin{matrix} Corner points & Corresponding value of Z (0, 0) & 0 (7, 0) & 91 (3, 4) & - 21 (0, 2) & 30 \leftarrow Manimum \end{matrix}$
Hence, the manimum value of Z is (-30)at (0,2).

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Minimise Z =13x -15 y subject to the contraints x+y≤7,2x−3y+6≥0,x≥0 and y≥0

Minimise Z =13x -15 y subject to the contraints $x + y \leq 7, 2 x - 3 y + 6 \geq 0, x \geq 0$ and $y \geq 0$