A linear programming problem is said to be infeasible if there is no solution that satisfies all the constraints.

A company's goal is to maximize profit, and they formulate a linear programming problem to decide how many chairs and tables to produce. However, due to certain constraints, they encounter infeasibility.

Constraint 1: Labor Hours - The company has a total of 40 labor hours available per day. Producing one chair requires 2 hours, and producing one table requires 3 hours.

Constraint 2: Raw Materials - The company has a limited amount of wood available for production. Producing one chair requires 4 units of wood, and producing one table requires 5 units of wood. The company has a total of 60 units of wood available.

Constraint 3: Demand - The company's market research indicates that they cannot sell more than 10 chairs and 15 tables per day.

Now, let's try to formulate the problem:

Objective: Maximize Profit (let's assume chairs sell for $100 each and tables for $150 each)

Variables:

x = Number of chairs to produce

y = Number of tables to produce

1.2x+3y≤40 (Labor hours constraint)

2.4x+5y≤60 (Raw materials constraint)

3.x≤10 (Demand constraint for chairs)

4.y≤15 (Demand constraint for tables)

Now, so when we graph these constraints on a coordinate plane, we might find that there is no feasible point that satisfies all constraints simultaneously. This could be because the demand constraint limits the production of chairs and tables to a point where the other constraints cannot be met. This situation represents infeasibility in real-life resource allocation problems, where the available resources and demand do not allow for a feasible production plan that maximizes profit

Credits: ChatGPT

set of values for the decision variables

Imagine you're trying to plan a road trip, but the gas money, food, and hotel costs are way more than your budget. That's like an infeasible situation your plan just doesn't work out with the resources you have. Another example: think about a class schedule where you can't fit in all the classes you need without overlapping times. It's a no go, just like infeasibility in math problems!

If there is no solution that meets all of the restrictions, the issue is said to be infeasible.

Resource Allocation Infeasibility:

Imagine a scenario where you need to allocate a set of resources to different projects. However, if the resources required by the projects exceed the available resources, the allocation problem becomes infeasible.