Question

Linear programming can be used in making product mix decisions. Explain why it is sometimes undesirable to concentrate on maximising sales of products with the highest unit contribution margin

Answer 1

To meet the demands of its customers, a company manufactures its products in its own factories (inside production) or buys them from other companies (outside production). Inside production is subject to some resource constraints: each product consumes a certain amount of each resource. In contrast, outside production is theoretically unlimited. The problem is to determine how much of each product should be produced inside the company and how much outside, while minimizing the overall production cost, meeting the demand, and not exceeding the resource constraints.

The statement of the problem must specify the set of products and the set of resources. For each product, we need to know the inside and outside production costs, and for each resource we need to know the available capacity of that resource. Finally, we need to know the consumption of resources by the different products.

Limitations of Linear Programming:

Linear programming has turned out to be a highly useful tool of analysis for the business executive. It is being increasingly made use of in theory of the firm, in managerial economics, in inter-regional trade, in general equilibrium analysis, in welfare economics and in development planning.

But it has its limitations:

1. It is not easy to define a specific objective function.

2. Even if a specific objective function is laid down, it may not be so easy to find out various technological, financial and other constraints which may be operative in pursuing the given objective.

3. Given a specific objective and a set of constraints, it is possible that the constraints may not be directly expressible as linear inequalities.

4. Even if the above problems are surmounted, a major problem is one of estimating relevant values of the various constant coefficients that enter into a linear programming mode, i.e., prices, etc

5. This technique is based on the assumption of linear relations between inputs and outputs. This means that inputs and outputs can be added, multiplied and divided. But the relations between inputs and outputs are not always linear. In real life, most of the relations are non-linear.

6. This technique assumes perfect competition in product and factor markets. But perfect competition is not a reality.

7. The LP technique is based on the assumption of constant returns. In reality, there are either diminishing or increasing returns which a firm experiences in production.

8. It is a highly mathematical and complicated technique. The solution of a problem with linear programming requires the maximization or minimization of a clearly specified variable. The solution of a linear programming problem is also arrived at with such complicated method as the ‘simplex method’ which involves a large number of mathematical calculations.

9. Mostly, linear programming models present trial-and-error solutions and it is difficult to find out really optimal solutions to the various economic problems.

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