# 急阿``微積分的英文題目，贈15點

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

Rating

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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