Question

Explain the meaning of the following terms: constraints, decision variables, feasible region and objective function. Explain their relevance to product mix decisions.

Answer 1

Constraints:

Constraints are the limitations imposed on the variables of a linear programming function. These are restrictions imposed on the possible values a decision variable can take. Generally, it is there in case of limited resources in case of an optimum utilization function.

It is not always maximum in nature - it can be minimum value as well.

Decision variables:

In order to even start solving any problem, firstly we have figure out our decision variables. These are the variables which are key in finding the solution for any linear programming problem - to decide what values of these variables will lead to a right solution (that's why they are called decision variables).

For simpler understanding, when we assume any amount/ quantity to be "X" or "Y" while solving any equation - those are the decision variables.

Feasible Region:

In simple words, it is a set of all feasible solutions on a graph. These points on this set satisfy all the problem constraints in case of an optimization problem. This is the region on the graph where the solution for any optimization is feasibly available and will lie.

Objective Function:

This can be understood as the final goal of creating any linear programming equation. This is the objective of making optimization decision.

For example: It can be profit maximisation, cost minimisation, time minimisation etc.

Relevance for product mix decision:

Product mix decisions are nothing but resource optimization problems - using the available resources for generating the best possible and profitable product mix for the company.

There can be constraints on resources available such as material supplied, labour hours available, bottleneck machinery or maximum quantity that can be supplied in the market without losing the desired profitability;

Also, the most obvious Objective function, in a product mix problem would be to maximize the profit and minimize the cost.

Decision variables are relevant for such decision making because there are majorly two variables - price of the product and quantity of the product

Also, the feasible region has to be understood and is relevant for the decision making because that's where the possible feasible solution for the optimum product mix will be found.