y=min{a*x1,b*x2},keepyconstant追问~1.y=min{a*x1,b*x2},keepyconstantBecausew1*x1+w2*x2>=(w1/a+w2/b)*min(a*x1,b*x2)=(w1/a+w2/b)*ysotheminimumcostis(w1/a+w2/b)*y为什么w1*x1+w2*x2>=(w1/a+w2/b)*min(a*x1,b*x2)=(w1/a+w2/b)*y还

Question

y = min{a*x1,b*x2},keep y constant 追问~
1.y = min{a*x1,b*x2},keep y constant
Because
w1*x1 + w2*x2 >= (w1/a+w2/b)*min(a*x1,b*x2) = (w1/a+w2/b)*y
so the minimum cost is
(w1/a+w2/b)*y
为什么
w1*x1 + w2*x2 >= (w1/a+w2/b)*min(a*x1,b*x2) = (w1/a+w2/b)*y
还有,
(w1/a+w2/b)代表是什么意思吖?

Answer 1

w1/a 就是w1除以a的意思,w2/b 就是w2除以b的意思,再把两项相加,就是w1/a+w2/b.
做的时候,因为y = min{a*x1,b*x2},所以就要想办法从总成本里凑出一个min{a*x1,b*x2}来.min表示两者中比较小的那个,所以
a*x1 >= min{a*x1,b*x2}
b*x2 >= min{a*x1,b*x2}
因此只需要凑出a*x1和b*x2.凑的办法是把第一项同时乘以和除以a,第二项同时乘以和除以b：
w1*x1 = (w1/a)*a*x1 >= (w1/a)*min(a*x1,b*x2)
w2*x2 = (w2/b)*b*x2 >= (w2/b)*min(a*x1,b*x2)
两项相加,就是
w1*x1 + w2*x2 >= (w1/a+w2/b)*min(a*x1,b*x2)
然后把y的定义代进来,就是
w1*x1 + w2*x2 >= (w1/a+w2/b)*y
(w1/a+w2/b)相当于加了权重的单位产出所需要的成本.