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The text in the image seems to outline a marketing decision scenario where Gilles Furniture, a company that sells furniture, is considering a promotional advertising budget to expand their customer base. The company is weighing the benefits of different forms of advertisement, such as TV shows, newspaper ads, and special promotions, while assessing their respective costs, viewership reach, and time spans.

Here is a transcription of the text from the image:

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**Gilles Furniture sells made-to-order furniture. The company is considering a large promotion advertising budget to spend among four media channels: their recurring TV show, newspaper ads, radio spots, and social media. Currently, the vast majority of the TV show is aimed at their mature or at least local audience, a sharp contrast to decisions you are making now to meet the budget you set. The TV show draws 20,000 interested viewers per airing, and the cost per airing is $3,000. The newspaper costs $1,800 and can be run up to seven days a week. Radio spots can be run 10 times per day at $60, and are heard by approximately 3,000 people per airing. Finally, social media can be purchased in segments of 10 days for $1,000, and is seen 20,000 times in this time. Set a budget and pick a media policy using the data above to maximize the media impact, but carefully choose where and how often to use this plan.**

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**Tasks:**
1. Define your variables.
2. What are the logical mathematical conditions to find if the problem is set up to determine the most efficient promotional outcomes?
3. Who are the customers?
4. What are the constraints?
5. What is the best decision?

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### Analysis:

The problem is asking you to distribute an advertising budget across different media to maximize reach while considering the cost and the audience impact of each media. Here’s a breakdown of the details:

- **TV Show:**  
  - Cost: $3,000 per airing  
  - Reach: 20,000 viewers per airing

- **Newspaper Ads:**  
  - Cost: $1,800 per day  
  - Reach: Not explicitly stated, but available for up to 7 days a week

- **Radio Spots:**  
  - Cost: $60 per airing  
  - Reach: 3,000 listeners per airing  
  - Can air up to 10 times per day

- **Social Media:**  
  - Cost: $1,000 per 10-day segment  
  - Reach: 20,000 views per 10 days

Now, you can define variables such as:
- $ x_1 $ = Number of TV show airings
- $ x_2 $ = Number of newspaper ad days
- $ x_3 $ = Number of radio spots
- $ x_4 $ = Number of social media 10-day segments

The total budget constraint would then be something like:

\[
3000x_1 + 1800x_2 + 60x_3 + 1000x_4 \leq \text{Total Budget}
\]

You will need to optimize for maximum audience reach, which could be represented as:

\[
20000x_1 + R_{\text{newspaper}}x_2 + 3000x_3 + 20000x_4
\]

where $ R_{\text{newspaper}} $ represents the reach of the newspaper ads, which is not explicitly provided.

### Would you like to proceed with setting up the optimization model or further explore the questions?

### 5 Related Questions:
1. How would you assign specific budget amounts to each advertising channel?
2. What impact would adding a new advertising medium have on your decision?
3. How can we quantify the reach of the newspaper ads?
4. What assumptions could you make about diminishing returns for each channel?
5. Could you modify the model to account for targeting a specific demographic?

**Tip:** Consider using linear programming or a similar optimization technique to allocate the budget efficiently.

Gilles Furniture is considering a large promotion advertising budget to spend among four media channels: their recurring TV show, newspaper ads, radio spots, and social media. The company needs to distribute the budget to maximize the media impact.

Learn how to allocate an advertising budget for Gilles Furniture across TV shows, newspaper ads, radio spots, and social media using optimization techniques. Maximize media impact within budget constraints with key insights into linear programming and audience reach.

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