情境,有個需求,配置給某AM工廠多少產量,可以最小化生產成本?
Assume AM Fixed Cost is a const.
AM Fixed Cost + AM Variable costs = TCO1
CM Fixed Cost + AM Variable costs = TCO2
Min TCO1 + TCO2
= Min (AM Fixed Cost + AM Variable costs + CM Variable costs )
= Min (AM Variable costs + CM Variable costs)
= Min (AM P * AM Q + CM P * CM Q)
= MIN (AM P(Q) * AM Q + CM P * CM Q)
= MIN P1(Q1)*Q1 + P2 * (Total Allocation - Q1)
= MIN P1(Q1^2) + P2TA - P2Q1
= MIN P1(Q1^2) - P2*Q1
= Q1 (MIN P1(Q1) - P2)
= 0
Ans : MIN Cost is happened at P1(Q1) = P2
以上就是理解數學建模的魔力計算出的結果,非憶測,而是能用數學證明!
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