$15\mathrm{.}7$ For Winnipeg Police Department: $15\mathrm{.}7$ The Winnipeg Police Department has five detective squads available for assignment to five open crime cases. The chief of detectives, Paul Kuzdrall, wishes to assign the squads so that the total time to conclude the cases is minimized. The average number of days, based on past performance, for each squad to complete each case is as follows:

Each squad is composed of different types of specialists, and whereas one squad may be very effective in certain types of cases, it may be almost useless in others

$($a$)$ Solve the problem by using the assignment method.

$($b$)$ Assign the squads to the above cases, but with the constraint that squad $5$ cannot work on case E because of a conflict.