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May 02, 2023

Answers:

Objective

The purpose of this advertising campaign is to reach maximum number of people through tv advertisement and social media campaign. Therefore, the objective of this linear programing is to optimize number of people reached through advertising campaign following constraints applicable for this program.

Constraints

Following constraints are applicable for this advertising program:

  • Total available budget is $30k and no additional budget is available which means that this proposed advertising campaign has to be completed within this allocated budget.
  • While the purpose is to allocate budget effectively between these two medium for advertising campaign, at least $10k budget has to be allocated to each of these advertising mediums as per requirements.

Decision Variables

Decision variables in context of linear programming is those variables that need to be determined and for this advertising program, decision variables are amount to be allocated to each advertising medium while maximizing number of people reached through these advertising programs.

Analysis Of Linear Programming

Following is the mathematical representation of this linear program:

$X1k = budget allocated for advertising through social media campaign

$X2k is budget allocated for tv advertising campaign.

As per given data, with each $1k that spent on social media campaign, 15 people are reached, and for tv advertising campaign, 10 people are reached with each $1k spent for advertisement.

Objective Function

Maximize: Z = 15X1 + 10X2

Subject to:

Constraint 1: X1 + X2 ≤ 30  

Constraint 2: X1 ≥ 10

Constraint 3: X2 ≥ 10

X1, X2 ≥ 0                                                          

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