Utilizing Linear Programming (LP) for Marketing and/or Consumer Research
Question one
Linear programming (LP) also referred to as linear optimization is a mathematical method used to determine an appropriate way for achieving the best outcome (such as lowest cost or maximum profit) in a particular mathematical model as linear relationships represented for some list of requirements (Gärtner & Matoušek, 2006). Nowadays, linear programming has become the most popular mathematical technique utilized in solving a variety of marketing and/or consumer research problems (Roos et al., 2006). Companies gain a major benefit by utilizing linear programming for marketing research which includes helping marketing managers across many fields of the economy to allocate an advertising budget that is fixed to various advertising media (Vanderbei, 2008).
Question two
An example of how linear programming can be used in marketing and/or consumer research includes solving a media selection problem. In this example a weekly budget for advertising should be $8,000 and 4 types of advertising media should be used with budgetary allocations shown in table below.
Decision: How many adverts should be allocated to each type of advertising media?
Objective: Maximize audience reached
| Advertising Options | ||||
| Radio (prime time) | Radio (afternoon) | Newspaper | TV Spot | |
| Audience Reached (per ad) | 2,400 | 2,800 | 8,500 | 5,000 |
| Cost (per ad) | $290 | $380 | $925 | $800 |
| Max Ads Per week | 25 | 20 | 5 | 12 |
Other restrictions include: Spending no more than $1800 on radio and having at least 5 radio spots per week.
Decision Variables
P = represents the number of radio spots per week (prime time)
A = represents the number of radio spots per week (afternoon)
N = represents the number of newspaper adverts per week
T = represents the number of TV spots per week
Objective Function (in the number of reached audience)
Max 2400P + 2800A + 8500N + 5000T
After the above expression is subjected to the constraints the resulting expressions are:
Budget is $8000: 800T + 925N + 290P + 380A 8000
At Least 5 Radio Spots per Week: P + A 5
No More Than $1800 per Week for Radio: 290P + 380A 1800
Max Number of Ads per Week for each advertising media is shown below:
P 25 N 5
A 20 T 12
Finally nonnegativity T, N, P, A 0
References
Gärtner, B., & Matoušek, J. (2006). Understanding and Using Linear Programming, Berlin: Springer-Verlag.
Roos, C., Terlaky, T., & Vial, J. (2006). Interior Point Methods for Linear Optimization, 2nd ed. Berlin: Springer-Verlag.
Vanderbei, R.J. (2008). Linear Programming: Foundations and Extensions, 3rd ed. Berlin: Springer-Verlag.
Last Completed Projects
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