Consider a database system that serves transactions of $2$ distinct kinds. Each query transaction requires $35$ ms of CPU processing and reading $230$ blocks from disk $($where each block occupies $4$KB$,$ and the disk can deliver $100$ MB$/$s$).$ Each update transaction requires $0\mathrm{.}3$ms of CPU processing, reading $1$ block from disk, and it also requires sending a log record to a dedicated archival storage, an operation which occupies this resource for $30$ ms$.$ Each client generates transactions without any think time between one response and the next request. $($a$)$ Suppose that each client generates requests for which the transaction mix consists of $25\%$ update transactions and $75\%$ query transactions. If there are $3$ clients, use the $$lowload bounds$$ to estimate the throughput and latency obtained. $($b$)$ Still with $25\%$ update transactions, what is the largest number of clients for which average response time will be below $2$s$?$