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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
≤
4
,
x
≥
0
,
y
≥
0
,
then
Z
max
is equal to
A
12
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B
16
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C
20
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D
24
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Solution
The correct option is
B
16
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 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
→
maximum
Hence, the maximum value of
Z
is
16
at the point
B
(
0
,
4
)
.
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0
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