The question gave you information that forces you into a specific type of distribution system. It told you the mechanical equipment was 480 volts. It also told you that the lights and convenience outlets were 120 volts, but that part would have been obvious anyway. So part of the answer is, as given in the question, that you need both 480 volts and 120 volts.
The question also gave you something important that is not obvious to the general public. They said that the mechanical equipment was three phase, but they didn't have to tell you that. That is because the question said that the mechanical equipment was 100 horsepower. They don't say how many machines there are, and how big the biggest would be. But it is a very safe bet that the biggest is bigger than 1 horsepower. That is significant because any motor that is bigger than 1 horsepower would almost certainly be a three-phase motor, rather than a single phase motor. So now you know that you need a 480 volt, three phase power system.
The other part of the question requires you to do something with the information that gave you concerning the loads. If you add up their list of loads, you will get 20,000 (lighting) plus 100,000 (motors) plus 20,000 (for 1 watt per square foot), for a total of 140,000 VA. I don't know if they taught you the following tidbit, but for a 480 volt, three phase system, you determine the amps by first dividing VA by 480, and then dividing the result by 1.732 (the square root of three). I get a result of about 168 amps. Therefore, you would need at least a 200 amp service.
Finally, they said the single phase load was 40,000 VA. The next higher size transformer (to go from 480 volts to 120 volts) is 45 KVA.
So my answer would be that you need a 200 amp, 480 volt, three phase service, and that you need at least a 45 KVA, 480-120/208V, three phase transformer.
One important note: The question gave you information that would be of interest to a buyer. However, that information is not what electricians and electrical engineers use as a basis for calculating the required service. We use similar information, and we have a calculation process that allows us to take credit for the high probability that not everything will be running at the same time.
Did you get the "book answer" for the homework assignment yet? I am curious as to what they consider the "right answer" for this question.