[請益] 個經成本極小化問題

[tomoya0711 (現在不開心)]

Nadine has production function 2*X1+X2. If the factor
price are $8 for factor 1 and $5 for factor 2, how much
will it cost her to produce 70 units of output?

a.$1470
b.$280
c.$350
d.$910
e.$315

答案是b.

我的算法是：

TRS=X2/X1=8/5
X2=8/5*X1代入product function
→70=2*X1+8/5*X1
→X1=175/9 X2=280/9
cost=2*175/9+280/9=40.....

答案跟選項完全不符合阿!!
請問我的做法哪裡出錯了呢....?
希望版上的高手能幫幫忙解決我的疑惑
謝謝O_Q

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推 cutebodlol:求解是求min 8X1+5X2 st 70=2X1+X2
→ cutebodlol:因為是線性 所以要嘛全部生產X1
→ cutebodlol:要嘛全部生產x2 故X1=35 或是 X2=70
→ cutebodlol:然後看哪個生產成本低就選哪一個
→ tomoya0711:謝謝你^_^ 問題解決囉!!