If Z-3x-4y- subject to the constraints- x-y - 4- x - 0 - y - 0- then Zmax is equal to-1 mark-

The feasible region determined by the constraints x+y ≤ 4,x ≥ 0,y ≥0 is as follows. The corner points of the feasible region are O(0,0),A(4,0) and B(0,4). The ...

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

Byju's Answer

Standard XII

Mathematics

Constraints

If Z=3x+4y, s...

Question

If $Z = 3 x + 4 y,$ subject to the constraints: $x + y \leq 4,$ $x \geq 0,$ $y \geq 0,$ then $Z_{max}$ is equal to

[1 mark]

16

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

20

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

24

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

12

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

Open in App

Solution

The correct option is A $16$
The feasible region determined by the constraints $x + y \leq 4, x \geq 0, y \geq 0$ is as follows.

The corner points of the feasible region are $O (0, 0), A (4, 0)$ and $B (0, 4)$ . The values of $Z$ at these points are as follows.

Corner points $Z = 3 x + 4 y$

$O (0, 0)$ $0$

$A (4, 0)$ $12$

$B (0, 4)$ $16 \to maximum$

Hence, the maximum value of $Z$ is $16$ at the point $B (0, 4) .$

Suggest Corrections

Similar questions

Q. Maximize

Z = 3 x + 4 y

subject to the constraints:

x + y \leq 4, x \geq 0, y \geq 0

Q. If

Z = 3 x + 4 y,

subject to the constraints:

x + y \leq 4,

x \geq 0,

y \geq 0,

then

Z_{max}

is equal to

Q. Solve the following Linear Programming problems graphically:
1. Maximize

Z = 3 x + 4 y

Subject to the constraints :

x + y \leq 4, x \geq 0, y \geq 0

2. Minimize

Z = - 3 x + 4 y

subject to

x + 2 y \leq 8, 3 x + 2 y \leq 12, x \geq 0, y \geq 0

Q. Solve the following Linear programming problems graphically :
Maximize

z = 3 x + 4 y

subject to the constraints :

x + y \leq 4, x \geq 0, y \geq 0

Maximum value of $Z = 12 x + 3 y$ , subject to constraints $x \geq 0$ , $y \geq 0$ , $x + y \leq 5$ and $3 x + y \leq 9$ is

Join BYJU'S Learning Program

Corner points	$Z = 3 x + 4 y$
$O (0, 0)$	$0$
$A (4, 0)$	$12$
$B (0, 4)$	$16 \to maximum$

If Z=3x+4y, subject to the constraints: x+y≤4, x≥0, y≥0, then Zmax is equal to [1 mark]

If $Z = 3 x + 4 y,$ subject to the constraints: $x + y \leq 4,$ $x \geq 0,$ $y \geq 0,$ then $Z_{max}$ is equal to

[1 mark]