Optimization of a Thermal Cracker via Linear Programming (STUDY CASE 2)
Author's Data: Housam BINOUS
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

The solution provided in this notebook is in agrrement with the values reported by Edgar et al. (2001). The author has solved this problem using GAMS and obtained the similar results: 

            VARIABLE    x1                       =    60000.000
            VARIABLE    x2                       =        0.000
            VARIABLE    x3                       =        0.000
            VARIABLE    x4                       =        0.000
            VARIABLE    x5                       =    40000.000
            VARIABLE    x6                       =        0.000
            VARIABLE    x7                       =    32795.539
            VARIABLE    z                        =   369560.000

GAMS file is available from author upon request. 

Reference:
Edgar, Himmelblau and Lasdon in Optimization of Chemical Processes, McGraw-Hill International Edition, 2001

objectv = 2.84*x1-0.22*x2-3.33*x3+1.09*x4+9.39*x5+9.51*x6 ;
capacit = 1.1*x1+0.9*x2+0.9*x3+1.0*x4+1.1*x5+0.9*x6 ≤ 200000;
ethyl = 0.5*x1+0.35*x2+0.25*x3+0.25*x4+0.5*x5+0.35*x6 == 50000;
propyl = 0.01*x1+0.15*x2+0.15*x3+0.18*x4+0.01*x5+0.15*x6 == 1000 ;
ethan = 0.4*x1+0.06*x2+0.04*x3+0.05*x4-0.6*x5+0.06*x6 == 0 ;
propan = 0.1*x2+0.01*x3+0.01*x4-0.9*x6 == 0;
heat = -6857.6*x1+364*x2+2032*x3-1145*x4-6857.6*x5+364*x6+21520*x7 == 20000000;
bound1 = x1≥0;
bound2 = x2≥0;
bound3 = x3≥0;
bound4 = x4≥0;
bound5 = x5≥0;
bound6 = x6≥0;
bound7 = x7≥0;

sol=Chop[Maximize[{objectv,capacit,ethyl,propyl,ethan,propan,heat,bound1,bound2,bound3,bound4,bound5,bound6,bound7},
{x1,x2,x3,x4,x5,x6,x7}]]

Off[General::spell1]

Objectv=(objectv/.sol[[2]])-(5.38*x7/.sol[[2]])