NCERT Solutions

Maximise $\mathrm{Z}=3 x+4 y$ subject to the constraints : $x+y \leq 4, x \geq 0, y \geq 0$.

Minimise $\mathrm{Z}=-3 x+4 y$ subject to $x+2 y \leq 8,3 x+2 y \leq 12, x \geq 0, y \geq 0$.

Maximise $\mathrm{Z}=5 x+3 y$ subject to $3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0$.

Minimise $\mathrm{Z}=3 x+5 y$ such that $x+3 y \geq 3, x+y \geq 2, x, y \geq 0$.

Maximise $\mathrm{Z}=3 x+2 y$ subject to $x+2 y \leq 10,3 x+y \leq 15, x, y \geq 0$.

Minimise $\mathrm{Z}=x+2 y$ subject to $2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0$. Show that the minimum of Z occurs at more than two points.

Minimise and Maximise $\mathrm{Z}=5 x+10 y$ subject to $x+2 y \leq 120, x+y \geq 60, x-2 y \geq 0, x, y \geq 0$.

Minimise and Maximise $\mathrm{Z}=x+2 y$ subject to $x+2 y \geq 100,2 x-y \leq 0,2 x+y \leq 200 ; x, y \geq 0$.

Maximise $\mathrm{Z}=-x+2 y$, subject to the constraints: $x \geq 3, x+y \geq 5, x+2 y \geq 6, y \geq 0$.

Maximise $\mathrm{Z}=x+y$, subject to $x-y \leq-1,-x+y \leq 0, x, y \geq 0$.