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Mathematics
Problem
Consider the linear programming problem: Maximise
Z
=
2
x
+
3
y
Z = 2x + 3y
Z
=
2
x
+
3
y
subject to
x
+
y
≤
6
,
x
+
k
y
≥
2
,
x
≥
0
,
y
≥
0.
x + y \le 6,\; x + k y \ge 2,\; x \ge 0,\; y \ge 0.
x
+
y
≤
6
,
x
+
k
y
≥
2
,
x
≥
0
,
y
≥
0.
For which value(s) of
k
k
k
is the optimal value of
Z
Z
Z
attained at the vertex
(
0
,
6
)
(0,6)
(
0
,
6
)
?
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