1. A pharmacy has determined that a healthy person should receive 70 units of proteins, 100 units of carbohydrates, and 20 units of fat daily. Given the six types of health food with their ingredients as shown in the table below, what blend of foods satisfies the requirements at minimum cost to the pharmacy? Create a mathematical model for this problem.

| Foods | Protein units | Carbohydrates units | Fat units | Cost per unit |
|-------|---------------|---------------------|-----------|---------------|
| A | 20 | 50 | 4 | 2 |
| B | 30 | 30 | 9 | 3 |
| C | 40 | 20 | 11 | 5 |
| D | 40 | 25 | 10 | 6 |
| E | 45 | 50 | 9 | 8 |
| F | 30 | 20 | 10 | 8 |

2. A local manufacturing firm produces four different metal products, each requiring machining, polishing, and assembling. The specific time requirements (in hours) for each product are as follows:

| Product | Machining (hours) | Polishing (hours) | Assembling (hours) |
|-----------|-------------------|-------------------|--------------------|
| I | 3 | 1 | 2 |
| II | 2 | 1 | 1 |
| III | 2 | 2 | 2 |
| IV | 4 | 3 | 1 |

The firm has available weekly: 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time. The unit profits on the products are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. Through other customers, the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Create a mathematical model for this problem. Assume unfinished pieces can be completed the following week.

3. A firm manufactures two products. The net profit on product 1 is Rupees 3 per unit, and Rupees 5 per unit on product 2. The manufacturing process involves two departments, D1 and D2. Each unit of product 1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. The machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced daily to maximize total profit? Create a mathematical model for this problem.

4. Discuss a few areas for the application of quantitative analysis in your organization or an organization you are familiar with for decision-making.

5. Take the data of the output of your organization, summarize it with a tool (like a bar chart, pie chart, etc.), and discuss the result. Provide your opinion on how to improve the results in the future.