The maximum range of objective function z = 3x + 2Y is [7,9], then the range of positive real number k is
x+y≥2
1≥x
So y ≥ 1
As shown in the picture
The black part is the area enclosed by the given conditions
When the line 3x + 2Y moves to the point a, Z takes the maximum value
Substituting the coordinates (1, K) of point a
Max(z)=3+2k
That is, 7 ≤ 3 + 2K ≤ 9
2≤k≤3
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