更新1:
how many units each of chemical X and chemicalY should the company purchase? how many units of chemical Z can be produced given these purchase?
更新2:
what is the value of λ (Lambda)? Interpret it in this situation.
Math problem
2008-03-11 6:21 pm
a chemical manufacturing plant can produce z units of chemical Z given x units of chemical X and y units of chemical Y, where z=500(x^0.6)(y^0.3). Chemical X costs $10 a unit and chemical Y costs $25 a unit. The company wishes to produce as many units of chemical Z as possible given a fixed budget of $2000.
回答 (2)
2008-03-11 8:04 pm
✔ 最佳答案
Setting the constraints:10x + 25y = 2000
2x + 5y = 400
So the Lagrange multipliers may be intepreted as follows:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/CrazyLag1.jpg
參考: My Maths knowledge
2008-03-11 10:02 pm
x = 5y, so y should be 80/3, rather than 2000/3. Please be careful.
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