This problem involves solving a system of linear equations to determine the number of units of products A, B, and C produced. Let's define the variables:

• $x$: number of units of product A
• $y$: number of units of product B
• $z$: number of units of product C

The problem provides the following constraints:

1. Total production constraint: $x + y + z = 120$

2. Time constraint: $2x + 4y + 6z = 400$

3. Profit constraint: $20x + 30y + 50z = 3300$

We will solve this system of equations.from sympy import symbols, Eq, solve

Define the variables

x, y, z = symbols('x y z')

Define the equations

eq1 = Eq(x + y + z, 120) # Total production constraint eq2 = Eq(2x + 4y + 6z, 400) # Time constraint eq3 = Eq(20x + 30y + 50z, 3300) # Profit constraint

Solve the system of equations

solution = solve((eq1, eq2, eq3), (x, y, z)) solution{x: 50, y: 60, z: 10}{x: 50, y: 60, z: 10}successThe solution to the system of equations is:

• $x = 50$: The factory produces 50 units of product A.
• $y = 60$: The factory produces 60 units of product B.
• $z = 10$: The factory produces 10 units of product C.

This satisfies all the given constraints.

Would you like further details on how these equations were solved, or do you have any other questions?

Here are 5 related questions to consider:

1. What happens if the total production is increased to 150 units while keeping other constraints the same?
2. How would changes in profit per unit affect the solution?
3. What if an additional constraint is added, such as a minimum production requirement for each product?
4. Can this problem be solved graphically for two variables?
5. How can optimization techniques be used if the goal is to maximize profit?

Tip: When solving real-world optimization problems, always check for feasibility by ensuring that all constraints are satisfied in the solution.