Question

运筹学的一些问题

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Answer 1

In[1]:= Minimize[{3 x1 + 2 x2 + x3, x1 + x2 + x3 <= 6, x1 - x3 >= 4,
x2 - x3 >= 3, x1 >= 0, x2 >= 0, x3 >= 0}, {x1, x2, x3}]
Out[1]= {\[Infinity], {x1 -> Indeterminate, x2 -> Indeterminate,
x3 -> Indeterminate}}
无解，因为x1 - x3 >= 4，于是x1>=4。同理x2>=3。所以x1 + x2 + x3>=7。而这与x1 + x2 + x3 <= 6矛盾。故无解。
接下来的几题都有解！
In[3]:= Maximize[{2 x1 + 2 x2 + 4 x3, 2 x1 + 3 x2 + 5 x3 >= 2,
3 x1 + x2 + 7 x3 <= 3, x1 + 4 x2 + 6 x3 <= 5, x1 >= 0, x2 >= 0,
x3 >= 0}, {x1, x2, x3}]
Out[3]= {38/11, {x1 -> 7/11, x2 -> 12/11, x3 -> 0}}
In[5]:= Maximize[{2 x1 + 3 x2 - 5 x3, x1 + x2 + x3 == 7,

2 x1 - 5 x2 + x3 >= 10, x1 >= 0, x2 >= 0, x3 >= 0}, {x1, x2, x3}]
Out[5]= {102/7, {x1 -> 45/7, x2 -> 4/7, x3 -> 0}}

In[6]:= Minimize[{4 x1 + 2 x2, 3 x1 + x2 == 3, 4 x1 + 3 x2 - x3 == 6,

x1 + 2 x2 + x4 == 4, x1 >= 0, x2 >= 0, x3 >= 0, x4 >= 0}, {x1, x2,
x3, x4}]
Out[6]= {24/5, {x1 -> 3/5, x2 -> 6/5, x3 -> 0, x4 -> 1}}

In[7]:= Minimize[{5 x1 - 2 x2 + 3 x3 + 2 x4,

x1 + 2 x2 + 3 x3 + 4 x4 <= 7, 2 x1 + 2 x2 + x3 + 2 x4 <= 3, x1 >= 0,
x2 >= 0, x3 >= 0, x4 >= 0}, {x1, x2, x3, x4}]
Out[7]= {-3, {x1 -> 0, x2 -> 3/2, x3 -> 0, x4 -> 0}}

Answer 2

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