Iam teaching a class that has n teaching assistants, each of whom hold office hours outside, at javacity. the ith ta holds office hours starting at time si and ending at time ei . each ta holds exactly one office hour (which may last any amount of time, not necessarily one hour, and different tas may have different interval lengths, which may overlap with one another). attendance has been low because students, being ics majors, are afraid of the sun, so the department announces that all tas who do not have a student visit them this week will be fired . because all of our teaching assistants are awesome 2 , we want to ensure that none get fired. however, due to student fears of the sun, we want to minimize the total number of visits made to tas.

Consider a power plant with water as the working fluid that operates on an ideal rankine cycle. it has a net power output of 45mw. superheated steam enters the turbine at 7mpa and 500°c (h=3411.4 kj/kg; s=6.8 kj/kg k) and is cooled in the condenser at a pressure of 10 kpa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. (a) show the cycle on a t-s diagram (a right schematic is fine - you do not need to calculate the temperatures at each point); (b)-determine the work done by the turbine and the pump in kj/kg; (c)-the mass flow rate of water used by the power plant; (d)-the thermal efficiency of the cycle; (e)-the temperature rise of the cooling water. assume the cooling water is incompressible with cp 4.18 kj/kg°c.