Given that real numbers x and y satisfy 2x + y ≥ 43x + y ≤ 62x − y ≥ - 4, then the value range of Y − 2x − 2 is obtained______ ．

Given that real numbers x and y satisfy 2x + y ≥ 43x + y ≤ 62x − y ≥ - 4, then the value range of Y − 2x − 2 is obtained______ ．

The feasible region is shown in the shadow of the figure: the objective function y − 2x − 2 can be considered as the slope of OQ between the origin (2,2) and a point (x, y) in the feasible region. When the line passes through point a, its minimum value is - 74, then the value range of Y − 2x − 2 is [− 74, + ∞), so the answer is: [− 74, + ∞)

Given that real numbers x and y satisfy 3x ^ 2 + y ^ 2 = 6, find the value range of P = 2x + y

If 3x ^ 2 + y ^ 2 = 6, let x = √ 2sina y = √ 6cosa
So 2x + y = 2 √ 2sina + √ 6cosa
According to the auxiliary angle formula, the value range of P = 2x + y is [- √ 14, √ 14]

The value range of Z = x + 2Y satisfying the constraint condition x ≤ 2Y ≤ 2x + y ≥ 2 is Z ∈______ ．

The plane region represented by the inequality system is shown in the figure, because when the straight line z = x + 2Y passes through B (2,2) in the feasible region, Z is the maximum and the maximum is 6; when it passes through C (2,0), Z is the minimum and the minimum is 2. So the value range of the linear objective function z = x + 2Y is [2,6]. So the answer is: [2,6]

Let real numbers x and y satisfy the constraint condition x ≥ 1 and X ≠ 2Y ≥ 1x + 2Y − 5 ≤ 0, then the value range of Z = x + y − 1x − 2 is ()
A. （-∞，-1]∪[3，+∞）B. （-∞，-2]∪[3，+∞）C. [-1，3]D. [-2，3]

For the plane region satisfying the constraint condition x ≥ 1 and X ≠ 2Y ≥ 1x + 2Y − 5 ≤ 0, ∵ z = x + y − 1x − 2 = z = 1 + y + 1x − 2 means the slope of the line between the point in the region and (2, - 1) point plus 1, and ∵ when x = 1, y = 1, z = - 1, when x = 3, y = 1, z = 3 ∪ z = x + y − 1x − 2 is (- ∞, - 1] ∪ [3, + ∞), so a is selected