Given the cost matrix below: $(40$ pts$)$

and the probability of a test instance belonging to class $1$ is $p,$ find the threshold $t$ such that it

is optimal $($i$.$e$.,$ minimizing cost$)$ to classify the instance as $1$ if $pt$ and it is optimal $($i$.$e$.,$

minimizing cost$)$ to classify the instance as $0$ if $p.$