Gas turbine engines21 have the following radial assembly of nozzle guides located immediately upstream from each rotor. The purpose of the vanes is to spread flow uniformly over the rotor, which improves its efficiency materially.

During engine maintenance, the 55 old vanes are removed and replaced by new and refurbished ones i = 1,

c, 55 marked with previously assessed performance measures ai and bi of the two faces. The effect of each nozzle slot is greatly impacted by the sum of the a-value for the vane placed on one side and the b-value for the vane installed on the other. Maintenance personnel want to choose an (counterclockwise)

arrangement of vanes around the assembly to balance this performance by minimizing the total of squared deviations between each resulting a + b sum and known target value t.

Show that this vane arrangement task can be viewed as a traveling salesman problem and write an expression for the corresponding point i to point j costs.