小虎 asked in 科學數學 · 1 decade ago

急阿``微積分的英文題目,贈15點

第二題有答案,但是我想知道過程

希望有人可以幫我呀!我星期一要考試了

1. Marginal revenue...

by the demand equation brand of

P=100e-0.0001x (o≦x≦20000)

A.find the revenue function R (hint. R(x)=Px)

B.find the Marginal revenue function R

C.What is the Marginal revenue when x=10?

2.Max revenue..

Refer to 1

How many pair of gloves must be sold to yield a max revenue? Ans 10000

What will be the max revenue? Ans 367879

Update:

P=100e-0.0001x ,......-0.0001是指數唷,應該看的董八

1 Answer

Rating
  • 1 decade ago
    Favorite Answer

    1.

    (a)

    TR=P*Q=P*X=100 [exp(-0.0001X) ]* X

    where, X=[0,20000]

    (b)

    MR=dTR/dQ=d(P*X)/dX= d/dx { 100 [exp(-0.0001x)] *X}

    = 100 [ exp(-0.0001x) ] + 100 x [exp(-0.0001x)] * (-0.0001)

    = [100 - 100x *(-0.0001) ] * [exp(-0.0001x)]

    = [100-0.01x] * [exp(-0.0001x)]

    (c)

    x=10 代入 MR 中

    MR= (100-0.1) * exp(-0.001) = 99.8

    2

    (1)

    F.O.C.

    dTR/dX = MR = 0

    令MR=0 則 ,100-0.01X = 0 ,故X=10000

    S.O.C.

    d^2 (TR) / dx ^ 2 = dMR/dx <0

    (2)

    the max revenue : x = 10000 代入TR中

    TR=100 [exp(-1) ]* 10000 = 1000000* exp(-1) = 367879.41

    2006-03-12 21:28:50 補充:

    2-(1)-s.o.c 就是"再微"一次TR,即對MR微分一次。微出來的公式,用X=10000代入,如果是負數,就是極大值的概念了。

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