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If x − 2Y + 1 ≥ 02x − y − 1 ≤ 0, then the maximum value of S = x + y is______ ．
Draw the feasible region satisfying the constraint condition x − 2Y + 1 ≥ 02x − y − 1 ≤ 0, as shown in the figure below: from the figure, when x = 1, y = 1, s = x + y takes the maximum value of 2, so the answer is 2
Let X and y satisfy the constraint condition group 0 less than or equal to x less than or equal to 1 0 less than or equal to y less than or equal to 2 2x-y greater than or equal to 1, then t = the maximum value of 2y-x
Draw the constraint conditions on the coordinate axis (the area surrounded by three lines) draw the 0 = 2y-x line, translate along the y-axis direction, and the intercept (T / 2) with the y-axis is the largest (T / 2 is the largest) when there is an intersection with the area (usually, several special points in the area composed of the constraint conditions are brought in and compared, which are generally the vertices)
If x and y satisfy 2x + Y-1 ≤ 0, y ≥ 0, then the maximum value of X + 2Y is 0______ ．
Let z = x + 2Y get y = - 12x + Z2, and make the plane region corresponding to the inequality system, as shown in the figure (shadow part OAB): translate the straight line y = - 12x + Z2. It can be seen from the image that when the straight line y = - 12x + Z2 passes through point a (0, 1), the intercept of the straight line y = - 12x + Z2 is the largest, at this time, Z is the largest, z = 0 + 2 × 1 = 2, and the maximum value of X + 2Y is 2
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