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Mathematics
Mathematics
Problem
Maximize
Z
=
7
x
+
5
y
Z = 7x + 5y
Z
=
7
x
+
5
y
subject to the constraints
x
+
2
y
≤
8
,
3
x
+
y
≤
9
,
x
≥
0
,
y
≥
0
x + 2y \le 8,\; 3x + y \le 9,\; x \ge 0,\; y \ge 0
x
+
2
y
≤
8
,
3
x
+
y
≤
9
,
x
≥
0
,
y
≥
0
. The optimum value of
Z
Z
Z
and the point at which it occurs are a)
Z
=
27
at
(
1
,
4
)
Z = 27\, \text{at } (1,4)
Z
=
27
at
(
1
,
4
)
b)
Z
=
31
at
(
3
,
2
)
Z = 31\, \text{at } (3,2)
Z
=
31
at
(
3
,
2
)
c)
Z
=
29
at
(
2
,
3
)
Z = 29\, \text{at } (2,3)
Z
=
29
at
(
2
,
3
)
d)
Z
=
28
at
(
0
,
4
)
Z = 28\, \text{at } (0,4)
Z
=
28
at
(
0
,
4
)
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