已知实数x,y满足约束条件x+y-6≤0,x+2≥0,x-y-2≥0,则z=2x-y的最小值为

Question

已知实数x,y满足约束条件x+y-6≤0,x+2≥0,x-y-2≥0,则z=2x-y的最小值为

Answer 1

已知实数x,y满足约束条件x+y-6≤0,x+2≥0,x-y-2≥0,则z=2x-y的最小值为
解析：∵x,y满足约束条件x+y-6≤0,x+2≥0,x-y-2≥0
x+y-6=0 (1),x+2=0 (2),x-y-2=0 (3)
(1)(2)联立得点(-2,8),(1)(3)联立得点(4,2),(3)(2)联立得点(-2,-4)
x,y满足约束条件的可行域为直角坐标系中点(-2,-4),(4,2)及三直线圈成的右下方区域
Z(-2,-4)=0,Z(4,2)=6
∴z=2x-y的最小值为0