A. If they wish to maximize the number of exposures to working mothers, how many ads of each type should be purchased? What is the objective function, and system of constraints? **Problem 2: Advertising Optimization**General Supervisory Services has $12,000 available for advertising. The table below details the costs per ad and the number of people exposed to its ads for three different media platforms, with costs in thousands.| Ad Packages | Social Media | Radio | TV ||--------------|--------------|-------|----|| Cost | 2 | 2 | 4 || Total audience | 30 | 21 | 54 || Working mothers | 6 | 12 | 8 |- **Objective:** If the total available audience is 420,000, and the goal is to maximize the number of exposures to working mothers, determine how many ads of each type should be purchased. Formulate the objective function and the necessary system of constraints.- **Tasks:** - Set up and solve the problem using Excel. - Provide a detailed discussion on the solution and what it implies.- **Update:** If new estimates suggest media exposure to working mothers is: 6,000 (Social Media), 4,000 (Radio), and 8,000 (TV), adjust the optimization model accordingly.- **Discussion Task:** Write a paragraph discussing how altering parameters can impact variable values and optimization results. Participants are encouraged to explore different parameters.**Problem 3: Cost Optimization for Deli and Catering**A Deli and Catering company manages two menus: I and II, prepared at three different facilities (A, B, and C). Below are the summarized production capacities and weekly operating costs:| | A | B | C ||--------------|----|----|----|| I | 200| 200| 400|| II | 100| 200| 100|| Cost / week | $1000| $3000| $4000|- **Objective:** Determine the number of weeks each facility should operate to fulfill orders at minimal cost. Formulate the objective function and system of constraints.- **Tasks:** - Use Excel to model and solve the problem. - Provide a thorough explanation and interpretation of the solution.These exercises aim to develop learners' ability to apply optimization techniques and interpret results within practical business contexts.

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General Supervisory Services has $12,000 available for advertising. The following table gives the costs per ad and the number of people exposed to its ads for three different media (with costs in thousands).

General Supervisory Services has $12,000 available for advertising. The following table gives the costs per ad and the number of people exposed to its ads for three different media (with costs in thousands).

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

A. If they wish to maximize the number of exposures to working mothers, how many ads of each type should be purchased? What is the objective function, and system of constraints?

**Problem 2: Advertising Optimization**

General Supervisory Services has $12,000 available for advertising. The table below details the costs per ad and the number of people exposed to its ads for three different media platforms, with costs in thousands.

| Ad Packages | Social Media | Radio | TV |
|--------------|--------------|-------|----|
| Cost | 2 | 2 | 4 |
| Total audience | 30 | 21 | 54 |
| Working mothers | 6 | 12 | 8 |

- **Objective:** If the total available audience is 420,000, and the goal is to maximize the number of exposures to working mothers, determine how many ads of each type should be purchased. Formulate the objective function and the necessary system of constraints.

- **Tasks:**
- Set up and solve the problem using Excel.
- Provide a detailed discussion on the solution and what it implies.

- **Update:** If new estimates suggest media exposure to working mothers is: 6,000 (Social Media), 4,000 (Radio), and 8,000 (TV), adjust the optimization model accordingly.

- **Discussion Task:** Write a paragraph discussing how altering parameters can impact variable values and optimization results. Participants are encouraged to explore different parameters.

**Problem 3: Cost Optimization for Deli and Catering**

A Deli and Catering company manages two menus: I and II, prepared at three different facilities (A, B, and C). Below are the summarized production capacities and weekly operating costs:

| | A | B | C |
|--------------|----|----|----|
| I | 200| 200| 400|
| II | 100| 200| 100|
| Cost / week | $1000| $3000| $4000|

- **Objective:** Determine the number of weeks each facility should operate to fulfill orders at minimal cost. Formulate the objective function and system of constraints.

- **Tasks:**
- Use Excel to model and solve the problem.
- Provide a thorough explanation and interpretation of the solution.

These exercises aim to develop learners' ability to apply optimization techniques and interpret results within practical business contexts.

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