Maximizing Audience Exposure: General Motors’ Advertising Campaign Optimization

In the fiercely competitive automotive industry, reaching the right audience is paramount. For General Motors (GM), a renowned manufacturer of luxury cars and trucks, this task becomes even more crucial as they aim to connect with high-income individuals who represent their most likely customers. To achieve this, GM is embarking on an advertising campaign that spans various media channels such as newspapers, television, radio, and shows. However, as they set out to optimize their campaign, they must do so while staying within a predetermined budget and adhering to specific constraints.

Objective Function: Maximizing Total Audience Exposure

GM’s primary objective is clear: they want to maximize their total audience exposure. In mathematical terms, this objective can be represented as an optimization problem. They aim to find the best combination of placements across different media channels to achieve the highest possible exposure to their target audience.

The objective function is expressed as follows:

Here:

Xn: Number of placements in newspapers

Xt: Number of placements in television

Xr: Number of placements in radio

Xs: Number of placements in shows

In this equation, each variable represents the number of placements in a specific media channel, and the coefficients (78, 95, 45, and 15) indicate the exposure (in thousands) associated with each placement.

Constraints: Balancing Budget, Maximum Placements, and Exposure

To ensure a well-balanced and efficient advertising campaign, GM must operate within certain constraints:

Budget Constraint: GM has allocated a budget of $190,000 for their advertising campaign. This financial constraint is vital to prevent overspending. The cost of placements in each media channel multiplied by the number of placements must not exceed this budget:

Maximum Placements Constraint: To make the most of their advertising campaign, GM must consider the maximum number of placements available in each media channel. These constraints restrict the number of placements GM can utilize in each channel:

1. • Newspaper: Xn ≤ 75
   • Television: Xt ≤ 45
   • Radio: Xr ≤ 50
   • Shows: Xs ≤ 27Exposure Constraint: GM’s strategy dictates that the number of placements on radio and shows should not exceed 20 percent of the total placements. This constraint helps maintain a balance in exposure across various media channels:
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     Xr + Xs ≤ 0.20 * (Xn + Xt + Xr + Xs)


These constraints, taken together, ensure that GM operates within their budgetary limits, utilizes media channels effectively, and maintains a strategic balance in exposure to their target audience.

In conclusion, General Motors faces the challenging task of optimizing their advertising campaign to maximize audience exposure while working within a budget and adhering to constraints. By formulating this problem as an optimization model, GM can strategically allocate their resources to reach their desired audience effectively. This optimization approach not only enhances their advertising campaign but also helps them stay competitive in the luxury automotive market. As GM continues to refine its advertising strategy, this mathematical model will serve as a valuable tool in their decision-making process, ensuring that every advertising dollar is spent wisely to engage high-income men and women, their most likely customers, and secure their position in the industry.