已知非负数x,y,z满足(x-1)/2=(2-y)/3=(z-3)/4,记w=3x+4y+5z,求w的最大值与最小值.请帮我写出解答的过程.要完整的解答过程!谢谢
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![已知非负数x,y,z满足(x-1)/2=(2-y)/3=(z-3)/4,记w=3x+4y+5z,求w的最大值与最小值.请帮我写出解答的过程.要完整的解答过程!谢谢](/uploads/image/z/1345201-25-1.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9D%9E%E8%B4%9F%E6%95%B0x%2Cy%2Cz%E6%BB%A1%E8%B6%B3%28x-1%29%2F2%3D%282-y%29%2F3%3D%28z-3%29%2F4%2C%E8%AE%B0w%3D3x%2B4y%2B5z%2C%E6%B1%82w%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%8E%E6%9C%80%E5%B0%8F%E5%80%BC.%E8%AF%B7%E5%B8%AE%E6%88%91%E5%86%99%E5%87%BA%E8%A7%A3%E7%AD%94%E7%9A%84%E8%BF%87%E7%A8%8B.%E8%A6%81%E5%AE%8C%E6%95%B4%E7%9A%84%E8%A7%A3%E7%AD%94%E8%BF%87%E7%A8%8B%21%E8%B0%A2%E8%B0%A2)
已知非负数x,y,z满足(x-1)/2=(2-y)/3=(z-3)/4,记w=3x+4y+5z,求w的最大值与最小值.请帮我写出解答的过程.要完整的解答过程!谢谢
已知非负数x,y,z满足(x-1)/2=(2-y)/3=(z-3)/4,记w=3x+4y+5z,求w的最大值与最小值.
请帮我写出解答的过程.要完整的解答过程!谢谢
已知非负数x,y,z满足(x-1)/2=(2-y)/3=(z-3)/4,记w=3x+4y+5z,求w的最大值与最小值.请帮我写出解答的过程.要完整的解答过程!谢谢
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
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<=2/3
4k+3>=0,k>=-3/4
所以-0.5<=k<=2/3
Wmin=6*(-0.5)+26=23
Wmax=6*2/3+26=30
设(x-1)/2=(2-y)/3=(z-3)/4=k
x=2k+1,x>=0,k>=-1/2
y=2-3k,y>=0,k<=2/3
z=4k+3,z>=0,k>=-3/4
-1/2<=k<=2/3
w=3x+4y+5z
=3(2k+1)+4(2-3k)+5(4k+3)
=14k+26
k=2/3,w的最大值28/3+26=
k=-1/2,w的最小值19