Location Choice

Suppose that there are hot dog vendors that are deciding where on a street to locate (for simplicity assume that the street length is measured from 0 to 1). Customers are uniformly distributed across the street's length and will buy from whichever vendor is closest. What is the Nash Equilibrium?

a.(1/2, 1/2)b.(0 , 1) and (1 , 0)c.(1/4 , 3/4)d.(0 , 1)