$($a$)$ Consider three different processors P$1,$ P$2,$ and P$3$ executing the same instruction set. $P1$ has a $3GHz$ clock rate and a $\frac{C}{P}$I of $1\mathrm{.}5.P2$ has a $2\mathrm{.}5GHz$ clock rate and a $\frac{C}{P}$I of $1\mathrm{.}0.P3$ has a $4\mathrm{.}0GHz$ clock rate and has a $\frac{C}{P}$I of $2\mathrm{.}2.$

a$.$ Which processor has the highest performance expressed in instructions per second?

b$.$ If the processors each execute a program in $10$ seconds, find the number of cycles and the number of instructions.

c$.$ We are trying to reduce the execution time by $30\%$ but this leads to an increase of $20\%$ in the CPI. What clock rate should we have to get this time reduction?