$1.[10$ pts$]$ Consider a processor that runs at $2$ GHz and $1\mathrm{.}0$ Volt. When running a given CPU$-$bound program, the processor consumes $110$ W$,$ of which $20$ W 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 $0\mathrm{.}8$ V to $1\mathrm{.}2$ V$.$ 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