a$.)$ A Program consists of $10000$ floating point instructions and $50000$ integer instructions. Processor has a clock rate of $4\mathrm{.}0GHZ.$ Floating point instructions take $10$ cycles and integer instructions take $6$ cycle. How long does it for this processor to run the program? And calculate the average CPI.

b$.)$ Which of the following improvement options in the processor will take lesser time to execute the program if $($a$)$ the CPI of floating point instruction is reduced to $6$ and the integer takes the same time as the base or $($b$))$ the CPI of integer is reduced to $3$ and the floating point instruction takes the same time as the base. How much faster is the improved machine compared to the base machine