To find the total production of department A, we need to consider the production flow between the departments A, B, and C.
Given that department B produces 2 units from one unit of A and department C produces 2 units from one unit of B, we can calculate the total production of department A.
Let's assume the initial production of department A (before selling) as A1. Since A sold half of its production to department B and half to outsiders, we can calculate the production received by department B and the outsiders.
Production received by department B from A = A1/2
Production sold to outsiders from A = A1/2
Department B receives A1/2 units from department A. Since department B produces 2 units from one unit of A, the total production of department B can be calculated as:
Production of department B = (A1/2) * 2 = A1
Now, let's calculate the production of department C. Department C receives half of its production from department B, which we calculated as A1. Since department C produces 2 units from one unit of B, the total production of department C can be calculated as:
Production of department C = A1 * 2 = 2A1
Finally, the total production of department A is the sum of its initial production (A1) and the production received by department C (2A1):
Total production of A = A1 + 2A1 = 3A1
Therefore, the total production of department A is 3 times its initial production (A1).