Applying Mathematica in Decision 
Support Systems

Mathematica code as it appeard in Mathematica in Education,
Volume 2 Number 1, Fall 1992

Jerry M. Chin
Computer Information Systems Department
College of Business Admnistration
Southwest Missouri State University
Springfield, MO 65804
JMC808F@SMSVA.BITNET

(Mathematica version 2.1)

e1 = -L P000 + u P001 == 0;
e2 = - u P100 + u P101 == 0;
e3 = -(L+u) P001 + u P011 == 0;
e4 = -2 u P101 + L P011 + u P111 == 0 ;
e5 = -(L+u) P011 + u P111 + u Pb11 == 0;
e6 = -(L+u) P111 + L P011 == 0;
e7 = - u Pb11 + u P111 == 0;
e8 = P000+P100+P001+P101+P011+P111+Pb11 == 1;

vars = {P000,P100,P001,P101,P011,P111,Pb11};
eqns = {e1,e2,e3,e4,e5,e6,e8};

solns = Factor[ Solve[eqns,vars] ];

Table[{solns[[1,j,1]],Factor[solns[[1,j,2]] ]},
	{j,1,7}] //ColumnForm

Figure 1

AvgNum = Factor[Sum[1 solns[[1,i,2]], {i,2,3}]] + 
	Factor[2 Sum[solns[[1,i,2]], {i,4,5}]] + 
	Factor[3 Sum[solns[[1,i,2]], {i,6,7}]] //Together

Plot3D[AvgNum,{L,1,10},{u,1,8}];

Figure 2

sum = Sum[Factor[ solns[[1,j,2]] ],{j,1,5,2}]; //Simplify

Leff = Simplify[L  sum]
AvgWait = Simplify[AvgNum / Leff]

Plot3D[AvgWait,{L,1,10},{u,1,8}];