Two independent ice cream vendors own choose to stand at the point 0.1 (firm 0) and 0.8 (firm 1) in a 1-mile long beach. Every day there are 2000 beach-goers who come to the beach and distribute themselves uniformly along the water. Every beach-goer wants exactly one ice cream during the day and values the ice cream from both stands at $25. All of the beach-goers would rather be sunbathing or in the water, so they have the disutility to walking on the beach for $4 per mile. Both firms have a marginal cost of 2 dollars per ice cream.

1, If both firms charge the same prices of 10, figure out every day how many ice creams that each firm sells.

2, If firm 0 charges a price of 10, but firm 1 increases its price to 12, figure out every day how many ice creams that each firm sells.

3, If firm 0 charges a price of 10, but firm 1 decreases its price to 8, figure out every day how many ice creams that each firm sells