Problem $1$

Suppose you have a machine which executes a program Consisting of $30\%$ floating point multiply, $20\%$ floating point divide, $10\%$ floating point add and the remaining $40\%$ are from other instructions.

a$)$ Management wants the machine to run $2$ times faster. You can make the divide run at most $3$ times faster and the multiply run at most $5$ times faster and Add run $10$ times faster. Can you meet management's goal by making only one improvement, and which one?

b$)$ Robert has now taken over the company removing all the previous managers. If you can make two improvements only, what are they and what is the speed of the improved machine relative to the original machine?