[示範]賺P幣要這樣啦

[Falconeye (未識綺羅香)]

1. 最大收益處必使淨利函數 NP(x) 之導數為 0 , 由於 NP(x) = TR(x) - TC(x)
   所以 NP'(x) = TR'(x) - TC'(x)  即知 NP'(x) = 0 --> TR'(x) = TC'(x)

4. (1) TC(x) = x^2/30 + 20x + 480 = 28
       AC(x) = TC(x)/x = x/30 + 20 + 480/x
       AC'(x)= 1/30 - 480/x^2 = (x-120)(x+120)/30x^2
       故生產量為120單位時有最小AC

   (2) AC(120) = 120/30 + 20 + 480/120 = 28
       TC'(120)= 120/15 + 20 = 28
       AC(120) = 28 = TC'(120)

6. x = D(p) = 300-2p , TR(x) = xp = x arcD(x) = x(150-x/2) = 150x - x^2/2
   π= NP(x) = TR(x) - TC(x) = -x^2/2 + 142x -1000 , NP'(x) = -x + 142
   MAX π為 x = 142 , p = 150 - 142/2 = 79

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