Question

Save Score: 0 of 3 pts HW Score: 16.67 %, 3 of 18 pts 2 of 6 (2 complete)v Problem 15.9 21 Daniel Glaser, chairman of the Colege of San Antonio's business department, needs to assign professors to courses next semester. As a criterion for judging who d should teach each course, Professor Glaser reviews the past 2 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 2-year period, Glaser is able to record a course rating for each instructor. These ratings are shown in the /w folowing table. Question Help ETT er to Course Professor Finance Statistics Management Economics ess w.W. Fisher D. Golhar 60 55 50 80 40 ng v 55 85 65 Z. Hug N. K. Rustagi 60 55 75 70 ed 90 65 40 95 :/wm a) The optimal assignment of courses to professors that will maximize the overal teaching rating is: ver tc ness N. K. Rustagi Statistics Ing v ve vis Management D. Golhar Finance w.W. Fisher ved Economics Z Hug s//w The overall teaching rating of the assignment (enter your response as a whole number). wer td ign p partm ould te aniel Enter your answer in the answer box and then click Check Answer. ps /w 1 part remaining Check Angwa Clear Al aniel Gl ofessors to courses next semester. As a criterion for judging who should teach each course, Ps MacBook Air

Answer 1

This is an application of 'Assignment' optimization problem. Please use the following formulation in Excel to obtain the optimal solution.

E B D 1 Prof Course Fin Total Stat Mgmnt Econ 2 -SUM(C3.F3) |=SUM(C4F4) |=SUM(C5.F5) -SUM(C6F6) wWF 3 DG 4 ZH 5 NKR 6 Total -SUM(C3:C6)SUM(D3D6) SUM(E3E6) -SUM(F3F6) 7 8 Prof Course Fin Stat Mgmnt Econ 9 wWF 40 50 80 60 10 DG 55 85 65 55 11 70 ZH 60 75 55 12 NKR 90 65 95 40 13 14 =SUMPRODUCT(C3:F6,C10F13) Overall rating 15 Lu ) N

SC$15 Set Objective: To: O Value Of: O Max Min By Changing Variable Cells: $C$3:$F$6 Subject to the Constraints: $C$3:$F$6 binary $C$7:$F$7 1 $G$3:$G$6 1 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear, Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Solution

Prof \ Course	Stat	Mgmnt	Fin	Econ	Total
WWF	0	0	1	0	1
DG	0	1	0	0	1
ZH	0	0	0	1	1
NKR	1	0	0	0	1
Total	1	1	1	1
Prof \ Course	Stat	Mgmnt	Fin	Econ
WWF	50	40	80	60
DG	55	85	65	55
ZH	60	75	70	55
NKR	90	65	95	40
Overall rating	310

So, the optimal assignment is as follows:

Stat --> NKR
Mgmnt --> DG
Fin --> WWF
Econ --> ZH

Overall rating = 310