$1\mathrm{.}6$: Consider three different processors P$1,$ P$2,$ and P$3$ executing the same instruction set. P$1$ has a $3$GHz clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has a $2\mathrm{.}5$GHz clock rate and a CPI of $1\mathrm{.}0.$ P$3$ has a $4\mathrm{.}0$GHz clock rate and has a CPI 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?