$(06$ pts $)$ Nearly all new computers have multiple processors that allow the CPU to run part or all of a program in parallel. Suppose a CPU has dual cores. Each core runs at $2\mathrm{.}3.$ Since it has two processors, the CPU can execute two instructions per cycle or $4\mathrm{.}6$ billion instructions per second.

a$)$ Assuming maximum parallelism, how long would it take for the $G5$ to run a program requiring the execution of $100$ million instructions?

b$)$ Assuming maximum parallelism, how long would it take for the G$5$ to run a program requiring the execution of $500$ billion instructions?

c$)$ Redo parts a$)$ and b$)$ assuming the CPU could only execute instructions simultaneously $30\%$ of the time. Show the formula you used in this calculation.

Please answer fully and specifically.