Spatial Equilibrium

(Note that the spatial equilibrium is also a Nash Equilibrium. Each vendor tries to get the maximum number of customers.

Given:

There are two ice cream vendors on a linear beach of 10 yards long.

Consumers are evenly distributed along the beach, located at the end points and

spaced 3 feet apart.

Production costs are zero. Both vendors sell ice cream for $2.00

Consumers walk to the closest vendor to buy ice cream.

The cost to consumers of travel to the vendor is 1 cents per yard (money equivalent

of consumer's time). Note that one-yard equals to 3 feet.

New Information:

Each ice cream vendor charges $2 for per cone.

Both vendors sell the same ice cream.

Question

What are the socially optimal locations that minimize aggregate travel costs & show on a line diagram?