LONG ANSWER: 70 Marks . An electrical utility company must produce electricity to meet the de- mands of a city. The company is regulated by the city it must charge a xed price specied by the government and it must meet all demand at that price. The total demand for electricity over any 24 hour period is known with certainty to be 13 units; however this demand diers from day (6 AM to 6 PM) to night (6 PM to 6 AM). During the day hours, 9 units of electricity are demanded, while during the night 4 units are demanded. This too is known with certainty. The electric utility has the following production function for electricity: 9+: = (KR-)1\" where 2' = d(dey),n(night}, K is the size of the generating plant, E1 is the amount of fuel used in the plant during the day, F\" is the amount of fuel used at night, qd is the amount of electricity produced during the day, and q\" is the amount of electricity produced at night. The rm can vary its use of fuel from day to night, but it must build a single generating plant it cannot change the size of the plant from day to night. Say a unit of plant costs 3" per 24 hour period and a unit of fuel costs an. (a) Conditional on the plant size K how much fuel will the company use during the day (Pd) and night (PH)? (5) (b) What size of plant will the utility build