Infeasibility in linear programming models refers to a situation where there are no feasible solutions that satisfy all the constraints. Let's understand this concept in detail.

Feasible Solution:
A feasible solution in linear programming is a solution that satisfies all the given constraints. It is a point that lies within the feasible region, which is defined by the intersection of all the constraints.

Infeasible Solution:
On the other hand, an infeasible solution is a solution that violates one or more constraints. It is a point that lies outside the feasible region and cannot be achieved given the constraints.

Number of Solutions:
Now, let's discuss the number of solutions to a linear programming model that satisfies all the constraints. This can be classified into four possibilities:

1. At least 1 solution: In some cases, there may be only one feasible solution that satisfies all the constraints. This means that there is a unique optimal solution to the linear programming problem.

2. An infinite number of solutions: In certain situations, there might be an infinite number of feasible solutions that satisfy all the constraints. This occurs when the constraints are not restrictive enough to define a unique solution.

3. Zero solutions (Infeasible): Infeasibility occurs when there are no feasible solutions that satisfy all the constraints. This happens when the constraints are contradictory or when they overlap in such a way that no feasible region exists.

4. At least 2 solutions: It is possible to have multiple feasible solutions that satisfy all the constraints. In such cases, the objective function may have multiple optimal solutions, and the decision-maker can choose any of them.

Correct Answer:
In the given question, the correct answer is option 'C', which states that the number of solutions to the linear programming models that satisfy all the constraints is zero. This means that the given constraints are contradictory or overlapping in such a way that no feasible solution exists.

By understanding the concept of infeasibility and the possible number of solutions in linear programming, we can analyze the feasibility of a problem and determine whether it is solvable or not.