The Quantitative Methods department head zt a major midwestern university will b

Question

The Quantitative Methods department head zt a major midwestern university will be scheduling faculty toteach courses during the Autumn term. Four core courses need to be covered. THe four courses are ay the undergraduate (UG), master of business administration (MBA), master of Science (MS), doctor of Philosphy (Ph.D) levels. .

Four professors will be assigned to the courses, with each professor recieving one of the courses. Student evaluations of the professors are available from the 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. If the department head makes teaching assignments on maximizing the student evalaution ratings over all four courses, WHAT staffing assignements should be made?

Course

Professor UG MBA MS Ph.D

A 2.8 2.2 3.3 3.0

B 3.2 3.0 3.6 3.6

C 3.3 3.2 3.5 3.5

D 3.2 2.8 2.5 ---

Explanation / Answer

Simply consider the sum of the 18 possibilities (D cannot have the PhD class) and find the maximum sum.

The following table accomplishes this.

Note that I have the table at the bottom. Once I created the 18 possibilities, I used the lookup function to write the values to the cells.

I actually calculated the max of the sums at the bottom of the column so that I could write a function identifying the row whose sum matched the max.

The solution is UG=D, MBA=C, MS=A, PhD=B, which generates a max value of 13.3

UG MBA MS Ph.D Sum Max Prof. Eval. Prof. Eval. Prof. Eval. Prof. Eval. A 2.8 B 3 D 2.5 C 3.5 11.8 A 2.8 C 3.2 D 2.5 B 3.6 12.1 A 2.8 D 2.8 B 3.6 C 3.5 12.7 A 2.8 D 2.8 C 3.5 B 3.6 12.7 B 3.2 A 2.2 D 2.5 C 3.5 11.4 B 3.2 C 3.2 D 2.5 A 3 11.9 B 3.2 D 2.8 A 3.3 C 3.5 12.8 B 3.2 D 2.8 C 3.5 A 3 12.5 C 3.3 A 2.2 D 2.5 B 3.6 11.6 C 3.3 B 3 D 2.5 A 3 11.8 C 3.3 D 2.8 A 3.3 B 3.6 13 C 3.3 D 2.8 B 3.6 A 3 12.7 D 3.2 A 2.2 B 3.6 C 3.5 12.5 D 3.2 A 2.2 C 3.5 B 3.6 12.5 D 3.2 B 3 A 3.3 C 3.5 13 D 3.2 B 3 C 3.5 A 3 12.7 D 3.2 C 3.2 A 3.3 B 3.6 13.3 Y D 3.2 C 3.2 B 3.6 A 3 13 Professor UG MBA MS Ph.D 13.3 A 2.8 2.2 3.3 3 B 3.2 3 3.6 3.6 C 3.3 3.2 3.5 3.5 D 3.2 2.8 2.5 ---

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