數學建模的好處,最小化生產成本 - Data Science

Posted by: bart30508 | in Data Science | 2 months ago |

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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數學建模的好處,最小化生產成本 - Data Science

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