A manufacturer makes two products A and B, each of which is processed in two departments, production and finishing. Each A takes 3 hours to produce and six hours to finish, whereas each B takes 5 hours to produce and 2 hours to finish. How many units of A and B can be produced and finished if exactly 24 hours are available in each department and all hours must be used?

How did you get that answer? I can't come up with the equations, I got them but I didn't get that answer

To determine the number of units of products A and B that can be produced and finished within the given time constraints, we need to find the maximum number of units that can be processed in both the production and finishing departments.

Let's start by calculating the maximum number of units that can be produced in the production department using the available time.

In 24 hours, each unit of A takes 3 hours to produce, so the number of units of A that can be produced in the production department is 24 divided by 3: 24 / 3 = 8.

Similarly, each unit of B takes 5 hours to produce, so the number of units of B that can be produced in the production department is 24 divided by 5: 24 / 5 = 4.8. Since we cannot produce a fraction of a unit, we can produce only 4 units of B.

Next, let's calculate the maximum number of units that can be finished in the finishing department using the available time.

In 24 hours, each unit of A takes 6 hours to finish, so the number of units of A that can be finished in the finishing department is 24 divided by 6: 24 / 6 = 4.

Similarly, each unit of B takes 2 hours to finish, so the number of units of B that can be finished in the finishing department is 24 divided by 2: 24 / 2 = 12.

Now, we need to consider the production and finishing departments together to determine the final answer. Since the number of units should be limited by the department that can process the fewest units, we take the smaller of the two numbers for each product.

For product A, we have produced 8 units in the production department and can finish only 4 units in the finishing department. Therefore, the maximum number of units of A that can be produced and finished is limited to 4 units.

For product B, we have produced only 4 units in the production department but can finish 12 units in the finishing department. Therefore, the maximum number of units of B that can be produced and finished is limited to 4 units.

In summary, the manufacturer can produce and finish a maximum of 4 units each of A and B within the given time constraints.