Assume that for a given program $65\%$ of the executed instructions are arithmetic, $20\%$ are load$/$store$,$ and $15\%$ are branch. Given the instruction mix and the assumption that an arithmetic instruction requires $2$ cycles a load store instruction requires $6$ cycles and a branch instruction requires $3$ cycles find the average CPI.

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

b$.$ 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?

c$.$ For a $5\%$ improvement in performance how many cycles must a branch instruction take if load$/$store and arithmetic instructions are not improved?

d$.$ For a $5\%$ improvement in performance how many cycles must a load$/$store instruction take if branch and arithmetic instructions are not improved