Minimise Z-x-2 y subject to the constraints- 2 x-y - 3x-2 y - 6X - y - 0Show that the minimum of Z occurs at more than two points-

The feasible region under the given constraints is nbsp; The coordinates of corner points and values of Z are Corner points Z=x+2y (0, ...

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Standard XII

Mathematics

Reflection of a Point about a Line

Minimise Z=x+...

Question

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

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Solution

The feasible region under the given constraints is

The coordinates of corner points and values of Z are

Corner points $Z = x + 2 y$

$(0, 3)$ 6

$(6, 0)$ 6

From the above table minimum value of $Z = 6$
Now, compare the constraints and objective function.
We observe that the slope of the constraint $(x + 2 y \geq 6)$ and objective function is same, so $Z$ will be minimum at all the points which lie on the constraint line $(x + 2 y = 6)$ between the points $(0, 3)$ and $(6, 0)$ .

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Minimise Z=x+2y subject to the constraints; 2x+y≥3,x+2y≥6,x, y≥0. Show that the minimum of Z occurs at more than two points.

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