optimal expansion

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg457] optimal expansion
• From: Chengri Ding <ding at gis.uiuc.edu>
• Date: Sun, 12 Feb 1995 21:10:45 -0600

```Dear Mathgroup netters,

I am new to the mathematica, I have met a terrible problem. I want to find
optimal time and optimal capital expansion. I try to use FindMinimum command
but it does not work out. I hope experts from net can help me out, and very

The objective function is:

-k + 0.004*t*(93633.3333333333 + 529.9999999999999*t + t^2) +
(0.005000000000000001*(93633.3333333333*k*llt1 +
529.9999999999999*k*llt1^2 + 1.*k*llt1^3 - 93633.3333333333*k*t -
529.9999999999999*k*t^2 - 1.*k*t^3))/(0.75 + 1.*k)

I used FindMinimum and got a message saying :

Objective function 24524.7 + 0.00181818 (-1.22633 10  + <<3>>)
is not real at {t, k} = {50., 2.}.

The arguement I used in the FindMinimum is:
FindMinimum[test3[t,k],{t,50,80},{k,2,5}]

I used another way to find the solution to the problem by drive partial
derivative of the objective function, I got:

equ1 =  (0.003000000000000003*(93633.3333333332 - 31211.11111111114*k +
1059.999999999999*t - 353.3333333333332*k*t + 2.999999999999998*t^2 -
1.*k*t^2))/(0.75 + 1.*k)
equ2 =   (1.*(-0.5625 - 1.5*k - 1.*k^2 + 351.1249999999999*llt1 + 1.9875*llt1^2 +
0.00375*llt1^3 - 351.1249999999999*t - 1.9875*t^2 - 0.00375*t^3))/
(0.75 + 1.*k)^2

and then I used  NSolve[{equ1==0,equ2==0},{t,k}]
but it took too long to find the solution. It seems to me that two equations is
not too complicated but could not get solution. Original obective is
more complicate, in a sense that it includes transendental form, and I
was not able to find the solution because the mathematica said that a
transendental function in the equation is treated in algegraically.

I hope experts from the net can help me out and I very appreciate it.

thx again

chengri Ding
University of Illinois at Urbana-Champaign

```

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