已知非负数x,y,z,满足二分之x-1=三分之2-y=四分之z-3,记w=3x+4y+5z,求w的最大值与最小值.

Question

已知非负数x,y,z,满足二分之x -1=三分之2-y=四分之z-3,记w=3x+4y+5z,求w的最大值与最小值.

Answer 1

设(x-1)/2=(2-y)/3=(z-3)/4＝k
x-1=2k,x=2k+1
2-y=3k,y=2-3k
z-3=4k,z=4k+3
W=3(2k+1)+4(2-3k)+5(4k+3)
=6k+3+8-12k+20k+15
=6k+26
因为x>=0,y>=0,z>=0
2k+1>=0,k>=-0.5
2-3k>=0,k=0,k>=-3/4
所以-0.5