Higgins Coal produces coals from West Virginia. Their production cost of coal is $ 135 per ton (short ton). Higgins can ship their coals to their customers (power plants) through truck or rail. The truck's rate for shipping coals is $1.50 per mile per truck (capacity is 20 tons per truck). The rail shipping rate of coal through rail is $5 per mile per rail car (capacity is 100 tons per railcar) + $140 of fixed cost per car (not relevant to distance).

a. If the customer is willing to pay $200 per ton for coal, what is the maximal distance that Higgins's coal ships by truck and can still makes profits (profit >=0)?

b. If the customer is willing to pay $200 per ton for coal, what is the maximal distance that Higgins's coal ships by rail and can still makes profits (profit >=0)?

c. Please find the equal-cost distance that the landed cost per ton by truck is the same as the landed cost per ton by rail?