An electric utility uses natural gas as fuel for a large multi-unit power plant. With all units in-service, for a given hour the plant's fixed cost is $120,000 and its variable cost is $50 per megawatt demanded. Total revenue each hour in dollars varies with demand. TR is given by TR=150D-0.02D2 where D is megawatts demanded for a given hour:
Direct use of equations in text will result in zero credit. Develop all your equations and show all your work.
a. What is the hourly demand in megawatts that will maximize the total revenue?
b. What is the hourly demand in megawatts that yields the maximum profit?
c. What is the maximum profit?
d. What is the domain (range) of hourly megawatts demanded that will result in the plant being profitable (profit >0)?