MATLAB: Can objective function of a linear programming model contain a constant term

constant termlinear programmingobjective-function

LP model Objective function: Max Z = a1x1+a2x2+a3x3+a4x4+K

where, x1,x2,x3,x4 are variables and K is a constant x1- product price, x2- product cost, x3- substitute price, x4-import price, K- transportation cost(shipping & handling charges)per unit product

Best Answer

Conjecture:

x* is optimal for

Max Z = a1x1+a2x2+a3x3+a4x4+K

if and only if x* is optimal for

Max Z = a1x1+a2x2+a3x3+a4x4

Thus it is sufficient to consider objective functions without a constant term.

Best wishes

Torsten.

Related Solutions

MATLAB: How can i call array elements in a plot3 function

s=10;b=8/3; r=28;h=0.003; a=28
x=0;y=1; z=0; f=zeros(1,3); f=[x y z]; 
k=1;
for t=0:h:100 
    k1_x=a*(y(k)-x(k));
    k2_x=a*(y(k)-x(k))+(k1_x*h*0.5);
    k3_x=a*(y(k)-x(k))+(k2_x*h*0.5);
    k4_x=a*(y(k)-x(k))+(k3_x*h);
    x(k+1)=x(k)+(k1_x+2*k2_x+2*k3_x+k4_x)*h/6; 
    k1_y=x(k)*(r-z(k))-y(k);
    k2_y=(x(k)*(r-z(k))-y(k))+k1_y*h*0.5;
    k3_y=(x(k)*(r-z(k))-y(k))+k2_y*h*0.5;
    k4_y=(x(k)*(r-z(k))-y(k))+k3_y*h*0.5;
    y(k+1)=y(k)+(k1_y+(2*k2_y)+(2*k3_y)+(k4_y))*h/6; 
    k1_z=x(k)*y(k)-b*z(k);
    k2_z=(x(k)*y(k)-b*z(k))+k1_z*h*0.5;
    k3_z=(x(k)*y(k)-b*z(k))+k2_z*h*0.5;
    k4_z=(x(k)*y(k)-b*z(k))+k3_z*h*0.5;
    z(k+1)=z(k)+(k1_z+(2*k2_z)+(2*k3_z)+(k4_z))*h/6; 
    k=k+1;
end
    plot3(x,y,z); grid on; xlabel('x'); ylabel('y');
    zlabel('z'); title('Lorenz attractor');

MATLAB: How to properly sum 3D matrixes

Use this function:

function M=sumnd(M,dim)
s=size(M);
M=permute(M,[setdiff(1:ndims(M),dim),dim]);
M=reshape(M,[],s(dim));
M=sum(M,2);
s(dim)=1;
M=reshape(M,s);
end

Code:

A=sumnd(M,3) ;
A = simplify(A) ;

Result:

[ x1*y1*(z1 + z2 + z3), x1*y2*(z1 + z2 + z3), x1*y3*(z1 + z2 + z3)]
[ x2*y1*(z1 + z2 + z3), x2*y2*(z1 + z2 + z3), x2*y3*(z1 + z2 + z3)]
[ x3*y1*(z1 + z2 + z3), x3*y2*(z1 + z2 + z3), x3*y3*(z1 + z2 + z3)]

Best Answer

Related Solutions

MATLAB: How can i call array elements in a plot3 function

MATLAB: How to properly sum 3D matrixes

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