Maximise Z = 3x + 4y, 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 , and are (0,0),(1,0) and (0,1), respectively. |c|c| Corner points & Corresponding value of Z (0,0) & 0 (1,0) & 3 (0,1) & 4 ( max.) Hence, the maximum value of Z is 4 at (0,1)

Linear Programming — Class 12 Maths Solution

exemplar sa SA NCERT,Exemp,Q.2,Page,250

Question

Maximise $Z = 3x + 4y,$ subject to the constraints $x + y \le 1,x \ge 0,y \ge 0$.

Step-by-step Solution

Maximise $Z = 3x + 4y,$ Subject to the constraints

$x + y \le 1,x \ge 0,y \ge 0$

The shaded region shown in the figure as OAB is bounded and the coordinates of corner

$figure$

points ${\rm{O}},{\rm{A}}$ and ${\rm{B}}$

are (0,0),(1,0) and $(0,1),$ respectively.

$figure$

Hence, the maximum value of Z is 4 at (0,1)

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