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 appreciate your help. 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