Assume that for a given program $70\%$ of the executed instructions are arithmetic, $10\%$ are load$/$store$,$ and $20\%$ are branch.

$($a$)$

Given this instruction mix and the assumption that an arithmetic instruction requires $2$ cycles, a load$/$store instruction takes $6$ cycles, and a branch instruction takes $3$ cycles, find the average CPI.

$($b$)$

For a $25\%$ improvement in performance, how many cycles, on average, may an arithmetic instruction take if load$/$store and branch instructions are not improved at all?

$($c$)$

For a $50\%$ improvement in performance, how many cycles, on average, may an arithmetic instruction take if load$/$store and branch instructions are not improved at all?