Besides optimizing the shop mix, BCG has also been asked to provide a view on where Highroad should expand its footprint, out of a list of potential sites provided by the highway authority. In order to do this, a simple profit model was developed to forecast the profit impact of each potential addition to the network.For example, Highroad currently operates the only rest stop between the cities of Nashua and Lowell, code named C$1.$ Highroad is paying the government highway authority $$5,000$ per day for the concession $($right to operate$)$ for C$1.$Due to increasing traffic on the highway between the two cities, the highway authority is proposing to develop another rest stop $($code named C$2,$ situated as below$)$ and offering Highroad the rights to operate it$.$ The cost for the concession to operate C$2$ is also $$5,000$ per day.Your team has come up with a simple model to estimate revenues and profits for both rest stops. Based on the exhibit below, please answer the following four questions. Traffic from Nashua to Lowell $=100$ cars per hourTraffic from Lowell to Nashua $=100$ cars per hourBoth directions of traffic can turn off to C$1,$ and to C$2$ if it exists.From Nashua to C$2$ is $30$ miles, from C$2$ to C$1$ is $30$ miles, from C$1$ to Lowell is $40$ miles.The probability that a car will visit a rest stop increases by $1\%$ for every mile driven without encountering a rest stop or a city. For example, a car driving from Lowell to Nashua would have a $40\%$ chance of visiting C$1.$ If that car visits C$1,$ it would have a $30\%$ chance of also visiting C$2($if that exists$).$EconomicsEach car that visits a rest stop is expected to result in an average revenue of $$10$ to Highroad. Assume that for each rest stop, Highroad has only two items in its cost structure:$$ Concession fees $($$$5,000/$day$)$ Other operating expenses $($$$6,000/$day$)$ Question $1$: What is the current estimated profit per dat for C$1$ before C$2$ is build? Question $2$: What is the profit per day for the new rest stop C$2$ if it becomes operational? Question $3$: If C$2$ becomes operational, what will be the estimated profit per day for C$1?$