941 Roscoe Davis chairman of a colleges business department

[9-41] Roscoe Davis, chairman of a colleges business department, has decided to apply a new method in assigning professors to courses next semester. As a criterion for judging who should teach each course, Professor Davis reviews the past two years teaching evaluations (which were filled out by students). Since each of the four professors taught each of the four courses at one time or another during the twoyear period, Davis is able to record a course rating for each instructor. These ratings are shown in the table. Find the best assignment of professors to courses to maximize the overall teaching rating.

PLEASE PROVIDE A DETAIL SOLUTION.

Course

Professor

Statistics

Management

Finance

Economics

Anderson

90

65

95

40

Sweeney

70

60

80

75

Williams

85

40

80

60

McKinney

55

80

65

55

Solution

We want to maximize the overall rating which can be done by selecting the best rated professor in the subject,

we need to maximize

Z = Stats rating + Management rating + Finance Rating + Economics Rating with the constratint that each professor takes only one course

hence the best possible combination will be

Finance - Anderson

Statistics - Williams

Management - McKinney

Economics - Sweeney

Hence the overall score wil be equal to 95 + 85 + 80 + 75 = 335

Hence average score will be equal to 335/4 = 83.75