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?
2400
To solve this problem, we need to determine the maximum number of units of products A and B that can be produced and finished within the given time constraints.
Let's start by determining the number of units of product A that can be produced and finished. We have 24 hours in each department, so in the production department, we can produce a maximum of 24/3 = 8 units of A. In the finishing department, we have 24/6 = 4 units of A that can be completed.
Now let's move on to product B. In the production department, we can produce a maximum of 24/5 = 4.8 units of B. However, we cannot produce a fraction of a unit, so we round it down to 4 units. In the finishing department, we can complete 24/2 = 12 units of B.
Therefore, the number of units of A that can be produced and finished is 8 units in production and 4 units in finishing. For product B, we can produce 4 units in the production department and finish 12 units.
In summary, the maximum number of units of A and B that can be produced and finished within the given constraints is:
Product A: 8 units produced and 4 units finished
Product B: 4 units produced and 12 units finished