Suppose that there is a model with two constraints
1) 120x1+160x2 <=(less than or equal to)450
2) 3x1+10x2 <= 25
and there is a third constraint called min. requirement,
orginally this constraint is:
37x1+65x2 >= (greater than or equal to)120
I have to find all values of the right hand side of the gram requirement that make the model infeasible? How could I do that? What calculations do I use?
To determine all the values of the right-hand side (RHS) of the minimum requirement constraint that make the model infeasible, you can perform the following calculations:
1. Set up the linear programming problem with the given constraints and the minimum requirement as the objective function.
Objective function: min 37x1 + 65x2
Constraints:
1) 120x1 + 160x2 ≤ 450
2) 3x1 + 10x2 ≤ 25
3) 37x1 + 65x2 ≥ RHS (where RHS is the right-hand side of the minimum requirement)
2. Solve the linear programming problem with different values for the RHS of the minimum requirement constraint. Start with a lower bound value and progressively increase it.
3. If the linear programming problem becomes infeasible (i.e., there are no feasible solutions), note the specific value of the RHS at which this occurs. This value of the RHS makes the model infeasible.
4. Continue increasing the RHS until a feasible solution is found. Repeat this process until you have tested all possible values for the RHS.
By systematically testing different RHS values, you can identify the range of values that make the model infeasible.
Note: Depending on the complexity of the model, you may need to use linear programming software or tools to solve the problem. The steps provided here are a general guideline for finding the values that make the model infeasible.