There are three departments A,B and C. B produces 2 units from one unit of A, C produces 2 units from one unit of B. Both A and B sold half of there production to next department and half to the outsiders, then what is the total production of A?

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).