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You've shared a document detailing the advertising constraints for the Westchester Chamber of Commerce, including audience estimates, costs, and maximum media usage across television, radio, and online platforms. Here's a breakdown of the information provided:

- **Television**:
  - Audience per advertisement: 300,000
  - Cost per advertisement: $2,000
  - Maximum media usage: 10 times

- **Radio**:
  - Audience per advertisement: 54,000
  - Cost per advertisement: $300
  - Maximum media usage: 20 times

- **Online**:
  - Audience per advertisement: 120,000
  - Cost per advertisement: $600
  - Maximum media usage: 10 times

Additional constraints include:
- Radio advertisements must not exceed 50% of the total advertisements.
- Television should account for at least 10% of the total advertisements.
- The promotional budget is limited to $15,900.

The objective is to maximize total audience contact while adhering to these constraints and the budget limit. If you'd like to formulate a mathematical model or need calculations to determine the optimal number of advertisements for each medium, please let me know, and I can help with that.

Do you need help with a specific calculation or optimization model for this scenario? Here are a few things you might consider:

1. How many advertisements can be maximized within the budget while considering the cost and audience constraints?
2. What combination of media allocations will maximize the audience while adhering to the specific medium constraints?
3. What is the maximum possible audience reach if the budget is fully utilized?
4. How does adjusting the number of advertisements in one medium affect the overall budget and audience reach?
5. What is the minimum and maximum number of advertisements that can be run given the constraints?

**Tip**: When dealing with multiple constraints and an objective like maximizing audience, consider using linear programming, a method for achieving the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are given, along with a budget and additional constraints. The goal is to maximize total audience contact while staying within the budget and other restrictions.

Learn how to maximize audience reach through an optimal mix of television, radio, and online advertisements while staying within budget constraints. This problem focuses on linear programming, optimization, and media usage limitations. Ideal for advanced students studying business mathematics.

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