Question

I am sure that any company wants to maximize its profit and linear programming might be used to find an answer concerning the value of this profit. If you would want to build the linear programming problem that provides such answers, how many constraints would you add? Do you think that an increase in the number of constraints implies solving a more realistic problem

Answer 1

In every company resources are constraint ( Say raw material, employee hours, production capacity, etc. ). Just imagine a situation where you build linear programming with only constraints as employee hours and production capacity in such case profit maximization done by it is flawed.

Eg: Production capacity is 100 units but raw material available to do it is 50 units only. In this case since raw material is not taken as constraints you would assume that all 100 units be produced produced. But reality is that you can produce only 50 units as you have restrictions on raw material. Thus profit maximization is incorrect.

Thus only when all constraints are involved. Linear programming would give realistic solution to profit maximization. If not it is always flawed.

Note: This doesn't mean you add constraints which do not exist. So it is not about how many constraints you need to have, it is about whether you have included all relevant constraints pertaining to problem. It may be as less as 2 or as many as 100.