If Z - x - 2y- subject to the constraints- 2x - y- 3- x - 2y- 6- x- y - 0- then the minimum of Z occurs at

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, ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Graphical Method of Solving Linear Programming Problems

If Z = x + 2y...

Question

If $Z = x + 2 y$ , subject to the constraints: $2 x + y \geq 3, x + 2 y \geq 6, x, y \geq 0,$ then the minimum of $Z$ occurs at

only one point

No worries! We‘ve got your back. Try BYJU‘S free classes today!

two points

No worries! We‘ve got your back. Try BYJU‘S free classes today!

more than two points

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

minimum of

Z

is not possible

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C more than two points
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 $(6, 0)$ .

Suggest Corrections

Similar questions

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

Q. Show that the maximum of

Z

occurs at more than two points.
Maximise

Z = - x + 2 y

, subject to the constraints:

x \geq 3, x + y \geq 5, x + 2 y \geq 6, y \geq 0

Q. Minimize

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 points.

Q. 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.

Q. Maximise

Z = - x + 2 y

, subject to the constraints:

x \geq 3, x + y \geq 5, x + 2 y \geq 6, y \geq 0

Join BYJU'S Learning Program

If Z=x+2y, subject to the constraints: 2x+y≥3, x+2y≥6, x, y≥0, then the minimum of Z occurs at

If $Z = x + 2 y$ , subject to the constraints: $2 x + y \geq 3, x + 2 y \geq 6, x, y \geq 0,$ then the minimum of $Z$ occurs at