There are three work centers (A, B, and C) in a factory that can each fit into any of three spaces (1, 2, and 3) off the corridor behind the processing equipment. The distance from 1-2 is 10 feet, 2-3 is 30 feet, and 1-3 is 40 feet. The matrix of work (trips per day) at the three centers are shown in the following table. Assume that each trip must be a round-trip (from 1 to 2 and back, for example). Find the optimal assignment that minimizes distance traveled.

There are three work centers (A, B, and C) in a factory that can each fit into any of three spaces (1, 2, and 3) off the corridor behind the processing equipment. The distance from 1-2 is 10 feet, 2-3 is 30 feet, and 1-3 is 40 feet. The matrix of work (trips per day) at the three centers are shown in the following table. Assume that each trip must be a round-trip (from 1 to 2 and back, for example). Find the optimal assignment that minimizes distance traveled. A B C A 20 50 B 30 O A-2, B-3, C-1 O A-2, B-1, C-3 O A-1, B-2, C-3 O A-1, B-3, C-2 A-3, B-2, C-1