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Mathematics
Problem
Consider the linear programming problem Maximise
Z
=
k
x
+
3
y
Z = kx + 3y
Z
=
k
x
+
3
y
subject to
x
+
y
≥
6
,
x
+
2
y
≤
8
,
x
≥
0
,
y
≥
0
x + y \ge 6,\; x + 2y \le 8,\; x \ge 0,\; y \ge 0
x
+
y
≥
6
,
x
+
2
y
≤
8
,
x
≥
0
,
y
≥
0
. For which values of
k
k
k
is the optimal value of
Z
Z
Z
attained at the vertex
(
4
,
2
)
(4,2)
(
4
,
2
)
of the feasible region? a)
k
<
1.5
k < 1.5
k
<
1.5
b)
k
=
1.5
k = 1.5
k
=
1.5
c)
k
≤
1.5
k \le 1.5
k
≤
1.5
d)
1.5
≤
k
≤
3
1.5 \le k \le 3
1.5
≤
k
≤
3
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