线性规划求解.docVIP

线性规划求解 实验目的 1. 线性规划求解的单纯形法的编程实现 2．掌握使用matlab、Lingo、Excel的线性规划求解功能求解线性规划问题。 实验内容 (1) max z=2*x1+3*x2-5*x3 x1+x2+x3=7 2*x1-5*x2+x3≥10 X1,x2,x3≥0 (2) min z=2*x1+3*x2+x3 x1+4*x2+2*x3≥8 3*x1+2*x2≥6 X1,x2,x3≥0 (3) max z=10*x1+15*x2+12*x3 5*x1+3*x2+x3≤9 -5*x1+6*x2 +15*x3≤15 2*x1+x2+x3≥5 X1,x2,x3≥0 (4) max z=2*x1-x2+2*x3 x1+x2+x3≥6 -2*x1+x3≥2 2*x2-x3≥0 X1,x2,x3≥0  实验步骤及结果 用Matlab编写单纯形法算法函数： function [x,z,flg,sgma]=simplexfun(A,A1,b,c,m,n,n1,cb,xx) % A,b are the matric in A*x=b % c is the matrix in max z=c*x % A1 is the matric in simplex table % m is the numbers of row in A and n is the con number in A % n1 is the nubers of artificial variables,and artificial variables are default as the last % n1 variables in x. % cb is the worth coefficient matrix for basic variables % xx is the index matrix for basic variables % B1 is the invers matrix for the basic matrix in simplex table.The initial % matrix is default as the last m con in the matrix A. x=zeros(n,1); z=0; B1=A1(:,n-m+1:n) sgma1=c-(cb*B1)*A [masg,kk]=max(sgma1) k=kk(1) flg=0 ll=0 while (masg0)(ll20) ll=ll+1 thita=1000+zeros(m,1) for i=1:m if A1(i,k)0 thita(i)=A1(i,k)\b(i) end end [r8,c8]=find(thita999) if sum(c8)m [mith,rr]=min(thita) r=rr(1) aa=A1(r,k); for i=1:m if i==r b(r)=b(r)/aa for j=1:n A1(r,j)=A1(r,j)/aa end end end for i=1:m if i~=r cc=A1(i,k) b(i)=b(i)-b(r)*cc; for j=1:n A1(i,j)=A1(i,j)-A1(r,j)*cc; end end end cb(r)=c(k) xx(r)=k; B1=A1(:,n-m+1:n) sgma1=c-(cb*B1)*A [masg,kk]=max(sgma1) k=kk(1) thita=100+zeros(m,1) else flg=3; masg=-1; x=unbou