by Serhiy Grabarchuk Jr
A company’s new 5-room floor is occupied by six employees in the ratio of 1:2:3 in three rooms, a Kitchen (K) and a Copier room (C). The total of all door-to-door employee-distances from the rooms to Kitchen is: 3×1 + 2×1.4 + 1×2.24 = 8.04 units.
Being a staunch trade union member, the floor planner wants to decrease the total as much as possible. The ratio of 1:2:3 should remain but employees can be placed in other rooms or exchanging with K and/or C.
What is the lowest total distance for the six employees the floor planner could reach?
The lowest total the floor planner can reach is below 6.5 in case the floor distribution is changed to the one show in the illustration. In that case the total of all door-to-door employee-distances is: 3×1 + 2×1 + 1×1.4 = 6.4 units.