If the objective function z-x-2y has to be optimized in subject to constraints - x-3- x-y-5- x-2y-6- y-0- Then which of the followings is correct

Given : objective function , Z=x+2y constraints : nbsp;x≥3, x+y≤5, x+2y≥6, y≥0 Plotting the graph of feasible region : From graph, our feasible region is ABC ...

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

Byju's Answer

Standard XII

Mathematics

Constraints

If the object...

Question

If the objective function $z = x + 2 y$ has to be optimized in subject to constraints : $x \geq 3, x + y \leq 5, x + 2 y \geq 6, y \geq 0.$ Then which of the following(s) is correct

Z_{m a x} = 7

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

Z_{m a x} = 4

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

Z_{m i n} = 0

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

Z_{m i n} = 6

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

Open in App

Solution

The correct option is D $Z_{m i n} = 6$
Given : objective function , $Z = x + 2 y$
constraints : $x \geq 3, x + y \leq 5, x + 2 y \geq 6, y \geq 0$
Plotting the graph of feasible region :

From graph, our feasible region is $A B C,$
Now value of objective function at corner points : $Z = x + 2 y$

Corner points : $(x, y)$ $Z = x + 2 y$

$A (3, 2)$ $7$

$B (3, \frac{3}{2})$ $6$

$C (4, 1)$ $6$

So, $Z_{m a x} = 7$ and $Z_{m i n} = 6$

Suggest Corrections

Similar questions

Q. For the objective function

Z = x + 2 y,

subject to constraints :

x - y \leq - 1, - x + y \leq 0,

which of the following(s) is not correct:

Q. If

z = 5 x + 2 y

subject to the following constraints :

x - 2 y \leq 2, 3 x + 2 y \leq 12, - 3 x + 2 y \leq 3, x \geq 0, y \geq 0,

then which of the following is/are true?

Q. Minimum value of objective function

z = 2.5 x + y

subject to the constraints:

x \geq 0, y \geq 0, 3 x + 5 y \leq 15, 5 x + 2 y \leq 10

Q. 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

Q. Maximise Z = − x + 2 y , subject to the constraints: .

Join BYJU'S Learning Program

Corner points : $(x, y)$	$Z = x + 2 y$
$A (3, 2)$	$7$
$B (3, \frac{3}{2})$	$6$
$C (4, 1)$	$6$

If the objective function z=x+2y has to be optimized in subject to constraints : x≥3,x+y≤5,x+2y≥6,y≥0. Then which of the following(s) is correct

If the objective function $z = x + 2 y$ has to be optimized in subject to constraints : $x \geq 3, x + y \leq 5, x + 2 y \geq 6, y \geq 0.$ Then which of the following(s) is correct