A heat engine operating on the Carnot cycle operates between two heat reservoirs of temperature $550C$ and $30C.$

a$)[2$ pts$]$ What is the efficiency of this engine?

b$)[6$ pts$]$ If the engine generates $1500$ J of work, how much heat does it absorb from the hot reservoir, and how much does it emit into the cold reservoir?

c$)[5$ pts$]$ Suppose you were able to change the temperature of one $($but only one$)$ reservoir by $5C.$ To get the greatest increase in efficiency, which temperature should you change and in which sense $($i$.$e$.$ hotter or colder$).$ Explain your reasoning.