Let$$s look into a single$-$core single$-$processor system with CPU speed of $1$GHz$.$ Attached to the chip of the processor there is only one level cache $($L$1)$ of size $32$KB $($Kilobytes$).$ The main memory connects to the CPU via a interconnect bus of finite speed. The DRAM $($main memory$)$ has size of $612$ MB$.$ The latency to L$1$ is $5$ cycles and the latency to main memory is $150$ cycles. In each memory cycle, the processor fetches $4$ words $($cache line has size of $4$ words$).$ Let$$s assume that each word has size of $4$ bytes. Each vector has dimension of $10,000$ elements and each element has size of one word. What is the peak achievable performance of the dot product of two vectors and when does it occur? What is the lowest performance of the dot product of two vectors and when does it occur? a$)$ Do not assume prefetching b$)$ Assume prefetching Note: Peak achievable performance is the maximum performance that can be achieved during execution of the above program: i$.$e$.,$ how many operations using the ALUs or $($Floating Point Operations per Second $-$ FLOPS$)$ in how many seconds or clock cycles? for $($i$=0$; i