Solving the Dual Linear Programming Problem

Earlier we considered the direct problem of linear programming:

In the system of inequalities, there should be the same type of signs “less than or equal”. Therefore, multiply the inequality by –1 and change the inequality sign to the opposite.

Limiting the integer number of variables is not required here.

The solution of the direct problem gave the following results:

X1=80; X2=1400;  F(x)=42400.

As a result of solving the dual problem, we get

Y1=0; Y2=33.3; Y3=220; Z(y)=42400.

An objectively conditioned score of Y1=0 indicates that we have an excess of wood. Y2=33.3, i.e. greater than zero. This suggests that this resource (labor) is fully used in an optimal way. The value of the objective function Z(y)= F(x)=42400. This indicates that the solution found is optimal.