Assume a program requires the execution of $5\mathrm{.}0$E$7$ FP $($floating$-$point$)$ instructions, $1\mathrm{.}1$E$8$ INT $($integer$)$ instructions, $8\mathrm{.}0$E$7$ L$/$S $($load$/$store$)$ instructions, and $1\mathrm{.}6$E$7$ branch instructions. The CPI for each type of instruction is $1,1,4,$ and $2,$ respectively. Assume that the processor has a $2$ GHz clock rate.a$)[2$ points$]$ If we want the program to run two times faster and can only optimize the CPI of FP instructions, what should be the final optimized CPI of FP instructions?b$)[2$ points$]$ If we want the program to run two times faster and can only optimize the CPI of L$/$S instructions, what should be the final optimized CPI of L$/$S instructions?c$)[2$ points$]$ If the CPI of INT and FP instructions is reduced by $40\%$ and the CPI of L$/$S and Branch is reduced by $30\%,$ how much speedup could the program gain?