Question

已知三个非负数A、B、C,满足3A+B-C=6,2A+B-3C=4,若m=3a-b-7c,求m的最大值和最小值

Answer 1

3A+B-C=6,(1)

2A+B-3C=4,(2)

(1)-(2):A+2C=2,A=2-2C

将其代入(1)

变换得B=6+C-3*(2-2C)=6+C-6+6C=7C

因A≥0,B≥0,C≥0

2-2C≥0,7C≥0

0≤C≤1

M=3a-b-7c=3(2-2C)-7C-7C=6-6C-14C=6-20C

当c=0时,M有最大值：M=6-20C=6

当c=1时,M有最小值：y=6-20=-14