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The quantitative methods department head at a major midwestern university will be scheduling faculty to teach courses during the coming autumn term. Four core courses need to be covered. The four courses are at the undergraduate $($UG$),$ master of business administration $($MBA$),$ master of science $($MS$),$ and doctor of philosophy $($Ph$.$D$.)$ levels. Four professors will be assigned to the courses, with each professor receiving one of the courses. Student evaluations of professors are available from previous terms. Based on a rating scale of $4($excellent$),3($very good$),2($average$),1($fair$),$ and $0($poor$),$ the average student evaluations for each professor are shown. Professor D does not have a Ph$.$D$.$ and cannot be assigned to teach the Ph$.$D$.$ level course.

Course

Professor UG MBA MS Ph$.$D$.$

A $3\mathrm{.}02\mathrm{.}83\mathrm{.}43\mathrm{.}4$

B $2\mathrm{.}62\mathrm{.}03\mathrm{.}12\mathrm{.}8$

C $3\mathrm{.}13\mathrm{.}03\mathrm{.}33\mathrm{.}3$

D $3\mathrm{.}02\mathrm{.}62\mathrm{.}3-$

If the department head makes teaching assignments based on maximizing the student evaluation ratings over all four courses, what staffing assignments should be made?

Professor A should teach the

$---$Select$---$

course. Professor B should teach the

$---$Select$---$

course. Professor C should teach the

$---$Select$---$

course. Professor D should teach the

$---$Select$---$

course.