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Byju's Answer
Standard VII
Mathematics
Subtraction of Algebraic Expressions
The minimum v...
Question
The minimum value of
3x + 5y
such that:
3
x
+
5
y
≤
15
4
x
+
9
y
≤
8
13
x
+
2
y
≤
2
x
≥
0
,
y
≥
0
is ........................
0
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Solution
The correct option is
A
0
Z = 3x + 5y
Let us consider
3
x
+
5
y
≤
15
...(i)
If 3x + 5y = 15
x = 0, y = 3
x = 5, y = 0
Let us consider
4
x
+
9
y
≤
8
...(ii)
x
=
0
,
y
=
8
9
x = 2, y = 0
Let us consider
13
x
+
2
y
≤
2
...(iii)
If 13x + 2y = 2
x = 0, y = 1
x
=
2
13
,
y
=
0
Comparing (ii) and (iii)
4x + 9y = 8 ...(ii)
13x + 2y = 2 ... (iii)
From (ii)
x
=
8
−
9
y
4
Putting in (iii)
13
(
8
−
9
y
)
4
+
2
y
=
2
104 - 117y + 8y = 8
109y = 96
∴
y = 0.88
Hence, x = 0.018
Checking at corner points:
∴
Z
(
0
,
8
9
)
=
3
(
0
)
+
5
(
8
9
)
=
4.44
Z(0.018, 0.88) = 3(0.18) + 5(0.88) = 4.454
Z
(
2
13
,
0
)
=
3
(
2
13
)
+
5
(
0
)
=
0.46
At (0, 0) Z = 0, so minimum value will be 0.
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Similar questions
Q.
Find the minimum value of 3x + 5y subject to the constraints
− 2x + y ≤ 4, x + y ≥ 3, x − 2y ≤ 2, x, y ≥ 0.