7. A firm called Terrible William's invented a revolutionary device called the Time Blaster that can temporarily stop time. Due to the innovations in technology, Terrible William's patented their time-stopping technology and the design of the Time Blaster, creating a monopoly through using legal barriers to entry for prospective firms. Terrible Williams' long-run cost curve is given by , where cost is measured in thousands of dollars. Market demand is given by , where price is also measured in thousands of dollars. a. Given that Terrible William's looks to maximize profit, how many Time Blasters should it produce? (8 points. Hint: the optimality condition is that .) b. Based on your answer to Part (a), what is the profit-maximizing price to charge? (6 points,) c. Determine the profit based on your answers from Parts (a)-(b). (6 points. Hint: Make sure to calculate total revenue AND total cost!)