To solve this problem, we need to set up a system of linear equations representing the time constraints for both the Assembly and Finishing departments. Let:

• $x$ represent the number of Basic products.
• $y$ represent the number of Advanced products.

The total time required for both products in the Assembly department is: $2x + 2.6y = 2551$ The total time required for both products in the Finishing department is: $2.7x + 2.15y = 2496$

We now solve this system of equations to determine $x$ and $y$.

First, we will use the method of substitution or elimination to solve these equations.The solution to the system of equations gives:

• $x \approx 369.47$ (Basic products)
• $y \approx 696.95$ (Advanced products)

Since we need to round down to the nearest whole number, the company should manufacture:

• 369 Basic units
• 696 Advanced units

Would you like more details on how these values were calculated, or do you have any further questions?

Here are five related questions for deeper understanding:

1. How does the total manufacturing time in each department affect the production numbers?
2. What happens if the available hours in the Assembly or Finishing departments change?
3. Could the company increase production by optimizing the manufacturing process?
4. What if the company introduces a third product with different time requirements?
5. How would an increase in demand affect production planning?

Tip: When solving systems of linear equations, substitution and elimination methods are powerful tools to handle real-world optimization problems like this one.