[8 pts] In studying a program, Eva Lu Ator identifies that it has three phases: It spends 50% of its time in the first phase; then it proceeds to the second phase, where it spends 10% of its time; and finally it enters the third phase, where it spends 40% of its time.
a. Eva first notices radical inefficiencies in the second phase. If she rewrites the second phase to be ten times faster, how many times faster will this new program be overall? (Show your work.)
b. Eva reconsiders: Rather than change the second phase, she looks very carefully at the first phase and discovers how to make it 25% faster. How many times faster will this new program be overall? (Show your work.)
c. If Eva has time to pursue only one of these two options, should she improve the first phase by 25% or the second phase by ten times?