## Optimizing Advertising for Maximum Audience ReachThe 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 as shown in the table below:| Constraint | Television | Radio | Online ||--------------------------|------------|-------|--------|| Audience per advertisement | 200,000 | 36,000 | 80,000 || Cost per advertisement | $2,000 | $300 | $600 || Maximum media usage | 10 | 20 | 10 |### Constraints and RequirementsTo ensure a balanced use of advertising media:1. **Radio advertisements** must not exceed 50% of the total number of advertisements authorized.2. **Television advertisements** should account for at least 10% of the total number of advertisements authorized.### Problem Statement**(a)** If the promotional budget is limited to **$25,100**, how many commercial messages should be run on each medium to maximize total audience contact?#### Input Fields for Solution:**Television:****Radio:****Online:**#### Budget Allocation:**Television Budget:****Radio Budget:****Online Budget:****Total Audience Reached:****(b)** By how much would audience contact increase if an extra $100 were allocated to the promotional budget? (Round your answer to the nearest whole number.)---**Note for Users:** Fill in the respective fields with your calculated values to determine the optimal number of advertisements for each category and the total audience reached.

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Description: ## Optimizing Advertising for Maximum Audience ReachThe 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

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A linear programming computer package is needed. 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 as shown. Constraint Television Radio Önline Audience per advertisement 200,000 36,000 80,000 Cost per advertisement $2,000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $25,100, how many commercial messages should be run on each medium to maximize total audience contact? Television Radio Online What is the allocation of the budget among the three media, and what is the total audience reached? Television Budget Radio Budget Online Budget Total Audience (b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? (Round your answer to the nearest whole number.)

A linear programming computer package is needed. 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 as shown. Constraint Television Radio Önline Audience per advertisement 200,000 36,000 80,000 Cost per advertisement $2,000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $25,100, how many commercial messages should be run on each medium to maximize total audience contact? Television Radio Online What is the allocation of the budget among the three media, and what is the total audience reached? Television Budget Radio Budget Online Budget Total Audience (b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? (Round your answer to the nearest whole number.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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## Optimizing Advertising for Maximum Audience Reach

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 as shown in the table below:

| Constraint | Television | Radio | Online |
|--------------------------|------------|-------|--------|
| Audience per advertisement | 200,000 | 36,000 | 80,000 |
| Cost per advertisement | $2,000 | $300 | $600 |
| Maximum media usage | 10 | 20 | 10 |

### Constraints and Requirements

To ensure a balanced use of advertising media:

1. **Radio advertisements** must not exceed 50% of the total number of advertisements authorized.
2. **Television advertisements** should account for at least 10% of the total number of advertisements authorized.

### Problem Statement

**(a)** If the promotional budget is limited to **$25,100**, how many commercial messages should be run on each medium to maximize total audience contact?

#### Input Fields for Solution:

**Television:**

**Radio:**

**Online:**

#### Budget Allocation:

**Television Budget:**

**Radio Budget:**

**Online Budget:**

**Total Audience Reached:**

**(b)** By how much would audience contact increase if an extra $100 were allocated to the promotional budget? (Round your answer to the nearest whole number.)

---

**Note for Users:** Fill in the respective fields with your calculated values to determine the optimal number of advertisements for each category and the total audience reached.

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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 as shown: Constraint Television Radio Online Audience per advertisement 100,000 16,000 35,000 Cost per advertisement $1,500 $250 $650 Maximum media usage 10 24 14 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0". No of commercial Advertisement Alternatives messages Television Radio Online What is the allocation of the budget…
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