已知实数x，y满足|2x+y+1|≤|x+2y+2|，且-1≤y≤1，则z=2x+y的最大值是_．
问题描述：
已知实数x，y满足|2x+y+1|≤|x+2y+2|，且-1≤y≤1，则z=2x+y的最大值是______．
答
先根据约束条件|2x+y+1|≤|x+2y+2|，-1≤y≤1，化间可得 ①2x+y+1≥0x+2y+2≥0x-y-1≤0，或 ②2x+y+1≥0x+2y+2≤0x+y+1≤0，或 ③2x+y+1≤0x+2y+2>0x+y+1≥0，或④2x+y+1≤0x+2y+2≤0x-y-1≥0．画出可行域，如...