The U.S. space agency, NASA, uses satellites for imaging celestial objects. The amount of fuel needed to reposition the satellites is a function of the sequence in which the objects are imaged. The matrix ‘cij ‘ below provides units of fuel consumption used to realign the satellites with the objects.

‘cij ‘ = ¶

- 1.5 2.6 3.1 4.4 3.8 1.9 - 4.7 5.3 3.9 2.7 2.9 4.3 - 3.5 5.4 6.2 3.4 5.1 3.6 - 2.2 1.9 4.4 3.4 5.9 2.4 - 2.6 3.1 2.7 6.5 1.1 2.9 -



Suppose that the cost per fuel unit is $12. Estimate a lower bound on the cost of imaging all six objects.