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<P>John Henry, an avid gardener, has found that the number of happy plants, <I >h</I>, depends on the amount of light, <I >l,</I> and water, <I >w</I>. The production function is as follows: <I >h</I> = min {<I >l</I>, 2<I >w</I>}.</P>
<P>If each unit of light costs <I >w</I><SUB>1</SUB>, and each unit of water costs <I >w</I><SUB> 2</SUB>, derive John’s cost function c (<I >w</I><SUB>1</SUB>, <I >w</I><SUB>2</SUB>, h).</P>
<P>我不知道怎么做啊…………</P>

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关键词：production function gardener depends Product function depends number amount plants

以下是引用orangeou在2007-7-15 19:22:00的发言：

John Henry, an avid gardener, has found that the number of happy plants, h, depends on the amount of light, l, and water, w. The production function is as follows: h = min {l, 2w}.

If each unit of light costs w₁, and each unit of water costs w ₂, derive John’s cost function c (w₁, w₂, h).

我不知道怎么做啊…………

C(H)=(W1+2W2)H

但是如果不在最优的决策点，例如L=5，W=2的时候，H还是4，但是C就应该是5W1+4W2了喔…………

min w1*L+w2*w

s.t. L>=h if L<w

w>=h if L>w