Response to the following problem:
A state highway department is planning the construction of a 50 mile, four lane toll road. It estimates that the construction cost (t=0) will be $200,000,000 and annual maintenance costs will be $1,000,000 per year forever. In addition, every 10 years in perpetuity, a major resurfacing will have to be carried out at a cost of $10,000,000. It is estimated that $6,000,000 cars and $600,000 trucks will use the road each year, and it is decided that the toll charged to a truck will be four times that of a car. Interest rate is 7%.
Determine what the toll should be for each car and truck to cover all expenses over an infinite planning period.
Note: The toll does not vary year-to-year.