There are three types of planes (1, 2, and 3) that use an airport runway.

Plane 1 needs a 100-yard runway, 2 needs a 150-yard runway, and 3 needs a 400-yard runway. The cost of maintaining a runway is equal to its length. Suppose this airport has one 400-yard runway used by all three types of planes and assume also that only one plane of each type will land at the airport on a given day. We want to know how much of the $400 cost should be allocated to each plane.
(a) Find the characteristic function.
(b) Find the least core and show it has only one allocation.