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, ...

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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

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two points

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more than two points

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minimum of

Z

is not possible

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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 $(6, 0)$ .

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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

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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