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The image you provided contains a problem related to optimizing the production of cookie boxes with specified dimensions. Here's a breakdown of the tasks:

1. **Context of the Problem**:  
   The company wants to design cookie boxes that maximize the number of cookies they can fit while minimizing production costs. The cookie box must be in a rectangular shape with fixed dimensions of 60 cm in length and 50 cm in width.

2. **Tasks Involved**:
   - **Elaboration of a Table**: The first task asks for a table to be created, which specifies the volume resulting from various possible heights of the cookie box. The dimensions of length and width are fixed (60 cm by 50 cm), so varying heights will give different volumes.
   
   - **Creation of a Graph**: The second task asks for a graph showing the volume obtained concerning the heights of the box. This graph will help visualize how the volume changes with different heights.

   - **Determine the Best Box Size**: Finally, the problem requires determining the optimal box height that allows the company to package the largest quantity of cookies while minimizing the cost.

### To proceed, I can help you with:
1. **Creating a table** that lists the volume for various heights.
2. **Generating a graph** that displays the relationship between box height and volume.
3. **Solving the optimization problem** to find the best height for maximum volume and minimum cost.

Would you like me to help with the calculations and graph generation?

#### Here are some follow-up questions to consider:
1. Should the box height have a specific range of values for the calculations?
2. Are there any constraints on the volume of the box?
3. Do you want a 2D or 3D graph for the volume analysis?
4. Is there a formula or specific cost structure for the box production that should be included in the calculations?
5. Should we assume the box shape remains a rectangular prism?

**Tip**: For optimization problems, identifying all constraints and understanding the relationships between variables is key to finding the best solution.

A company wants to initiate large-scale sales of cookies by selling in all major cities of the country. To maximize the number of cookies per box while minimizing production costs, they need to design a rectangular box with fixed dimensions (60 cm long by 50 cm wide). Tasks include: 1. Create a table showing the resulting volumes from various box heights. 2. Create a graph showing the volume based on the box height. 3. Determine the optimal box size that allows the company to sell the most cookies at the lowest cost.

Learn how to optimize the volume of a rectangular cookie box with fixed dimensions (60 cm by 50 cm) to maximize the number of cookies while minimizing production costs. This problem covers geometry and optimization concepts and is suitable for Grades 9-10.

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