A coffee house finds that its weekly profit P (measured in dollars) as a function of the price x (measured in dollars) it charges per cup of coffee is given by the function m, defined by m(x) = -300x +978x - 570 where P = m(x). a) Determine the maximum weekly profit and the price of a cup of coffee that produces that maximum profit. b) The profit function for Delish Coffee (another coffee house) is defined by the function h where h(x)=m(x-2.5). Does the function h have at the same maximum value as m? Explain. c) What is the price per cup of coffee that Delish Coffee must charge to produce a maximum profit? Explain. d) Describe the meaning of k(x) = m(x) - 115 and then compare/contrast the maximum value for each function.