$[10$ pts$]$ Consider a processor that runs at $2GHz$ and $1\mathrm{.}0$ Volt. When running a given CPUbound program, the processor consumes $110W,$ of which $20W$ is leakage $($leakage is constant with respect to temperature$).$ The program takes $50$ seconds to execute. Assume the processor can execute safely at voltages between $0\mathrm{.}8V$ to $1\mathrm{.}2V.$ Voltage and frequency follow a linear relationship $($i$.$e$.,$ if voltage doubles, frequency doubles as well$).$ Assume the CPU runs at the same temperature no matter what the voltage & frequency. Can you compute the following values:

a$.$ The smallest time it takes to execute the program.

b$.$ The highest power to execute the program.

c$.$ The lowest energy to execute the program