Benefits of utilizing linear programming (LP) for marketing research
Linear Programming
According to Bazaraa, Jarvis, and Sherali (2011), linear programming is a mathematical model with an objective function and constraints that can be used to make the right decisions on how a business can optimize an existing market and make sustainable profits.
Benefits
The model enables practical problems in marketing research to be solved using thousands of decision variables and constraints. The underpinning strength is to use an extreme point of a function to satisfy certain constraints (Bazaraa et al., 2011). Here, the problem constraints are linear and the function in the linear equation is referred to as the objective function because is used to optimize solutions for the marketing research problem.
Canonical nature of LP
The typical canonical nature of a linear programming problem is maximization (≤) and minimization (≥) of the linear programming problem. The model can be used to make decisions under conditions of certainty, uncertainty, and under those conditions of risk. Under uncertain conditions, the decisions can be made based on the maxima criteria, which provide the right optimistic criterion for decision making. Here, the pay-offs have to be considered depending on the random state of nature, and the value can be computed as follows:
α(maximum payoff) + (1- α) (minimum payoff)
How LP can be used for marketing and/or consumer research
Marketing research
Marketing research is scientific process business organizations use to gather information and establish the needs and wants of customers and the best methods of fulfilling them while ensuring to make sustainable profits (Zopounidis & Pardalos, 2010). The objectives are to enable the business organization to fine-tune the marketing mix to address customer needs and expectations with a balanced supply of products according to customer demands.
Decision making
The right decisions can be made using descriptive, diagnostic, and predictive research at the strategic, tactical, and operational levels by the business organization managers using the right market research information. Decision making based on the needs and requirements of the target market can be beneficial to the organization if the management optimizes the linear programming model.
Example
For instance, to conduct a marketing/consumer research program, an organization can decide to use various tools to reach the target audience and make the right decisions on the best combination of product features to address the customer needs and wants using the right media outlet (Zopounidis & Pardalos, 2010). The choice of media alternatives to select from depends on the budget allocation, restraints, and the total amount of money available to use. The media outlets consist of magazines, radio, social media, and other outlets that can be optimized to reach the market. Besides, the linear programming method can be used to determine the right advertising expenses among different advertising vehicles.
A typical example is where linear programming is used to determine the effectiveness of the available advertising alternatives using the following formula:
WAA = Adjusted audience (AA) x Exposure factor (E x F) x Evaluation Factor (E v F)
In the above formula, AA is the target audience, E × F is the fraction of the audience that reads the advertisement, and (E v F) is a subjective weight that is based on a scale of 0-1 score. Assume that 4 advertising vehicles have been considered, the objective function is expressed as:
Maximize total WAA= 
The formula can be added to excel, and an excel solver can be run to determine the right advertising vehicle to use.
References
Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2011). Linear programming and network flows. New York: John Wiley & Sons.
Zopounidis, C., & Pardalos, P. (2010). Handbook of multicriteria analysis. New York: Springer Science & Business Media.