a$)$ A benchmark program is run on a $400-MHz$ processor. The executed program consists of $2$ million instruction executions. The cycles per instruction $($CPI$)$ and instruction mix are given in a table below.

$\backslash$table$[[$Instruction Type,CPI,Instruction Mix $(\%)],[$Arithmetic and logic,$1,60],[$Load$/$store with cache hit,$2,18],[$Branch$,4,12],[$Memory reference with cache miss,$8,10]]$

Determine the effective CPI and millions of instructions per second $($MIPS$)$ of the processor.

b$)$ Briefly describe $3$ methods used to increase processor speed.