Question

运筹学：图片中这道题怎么做？

Answer 1

In[1]:= t =
Maximize[{30 a + 40 b, a >= b, 2 a + 3 b <= 30, 4 a + 2 b <= 36,
3 a + 4 b <= 24, 5 a + 3 b <= 30, b >= 0}, {a, b}]
{2 a + 3 b, 4 a + 2 b, 3 a + 4 b, 5 a + 3 b} /. t[[2]] // N
Out[1]= {240, {a -> 24/7, b -> 24/7}}

Out[2]= {17.1429, 20.5714, 24., 27.4286}

尽量满足条件求解，得知瓶颈在设备1，如果用两套设备1，接下来的瓶颈为设备2
In[3]:= t =
Maximize[{30 a + 40 b, a >= b, 2 a + 3 b <= 30, 4 a + 2 b <= 36,
3 a + 4 b <= 48, 5 a + 3 b <= 30, b >= 0}, {a, b}]
{2 a + 3 b, 4 a + 2 b, 3 a + 4 b, 5 a + 3 b} /. t[[2]] // N
Out[3]= {525/2, {a -> 15/4, b -> 15/4}}
Out[4]= {18.75, 22.5, 26.25, 30.}
于是把设备2也增加一套，
In[5]:= t =
Maximize[{30 a + 40 b, a >= b, 2 a + 3 b <= 30, 4 a + 2 b <= 36,
3 a + 4 b <= 48, 5 a + 3 b <= 60, b >= 0}, {a, b}]
{2 a + 3 b, 4 a + 2 b, 3 a + 4 b, 5 a + 3 b} /. t[[2]] // N
Out[5]= {420, {a -> 6, b -> 6}}

Out[36]= {30., 36., 42., 48.}

这时材料全用完，利润也超过了380.

Answer 2

解析： (1) 假设xsinx=(x+T)sin(x+T) 则， xsinx-xsin(x+T)=Tsin(x+T) x2cos(x+T/2)sin( 则，