PROBLEM $1$ Assume that a program has $410,000$ instructions. There are $4$ instruction classes in the program, and each class requires a certain number of clock cycles to execute, as shown below. a$)$ If the program execution time is $3\mathrm{.}14$s$,$ what is the clock cycle of the computer? At what frequency does the computer run? b$)$ Assume that a computer system has a processor with $16$ cores that can be used to solve a problem in parallel. $96\%$ of the code is parallelizable. Can the system achieve a speedup of $10?$ How many cores are needed for this performance?