A business has modeled the revenue over the next ten years to follow the model r(t) = t + 372 while their cost of manufacturing, for the same time period should follow the model c(t) = t^2 - 13t + 337 where the revenue and cost are measured in thousands of dollars, and t is measured in months. Assume t = 1 is the start of January, t = 2 is the start February, etc.
Calculate the following using the models above:
a) When will the company have their maximum profit? (Round to the nearest tenths place.)
b) What will their maximum monthly profit be?