The SCM department has four professors, Saba, Geoff, Tang and Daves. To schedule their teaching for the next semester, the department chair collected their prep time (in weeks) for each of the six courses (shown in table below). Each professor has to teach at least three courses, but no more than four. To meet students' need, the department needs to offer at least eight sections for Intro to SCM (business core course). The department also needs to offer one section for all the other courses.

	Intro to SCM	Project Mgt	Quality Mgt	Control	Logistics	Mgt Science
Saba	3	10	12	16	12	7
Geoff	4	19	2	10	8	18
Tang	5	11	4	14	14	3
Daves	4	11	4	15	17	15

The department chair wants to find the least time-consuming schedule for all professors. Let ij = number of sections of course j that Professor i is assigned to teach, where i = S (Saba), G (Geoff), T (Tang), D (Daves), and j = I (Intro to SCM), P (Project Mgt), Q (Quality Mgt), C (Control), L (Logistics), M (Mgt Science).

Sub-question 1: What is an appropriate objective function?____ ABCD____

A) Max Z =3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM +

5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM

B) Min Z =3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM +

5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM

C) Min Z =SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM +

TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM

D) Max Z =SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM +

TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM

Sub-question 2: Which of the following is an appropriate constraint? ____ ABCD____

A) DI + DP + DQ + DC + DL + DM = 3

B) SI + GI + TI + DI 8

C) SM + GM + TM + DM 1

D) SI + SP + SQ + SC + SL + SM 4

Sub-question 3: Which constraint ensures that Intro to SCM is offered as described? ____ ABCD____

A) SI + GI + TI + DI 8

B) SI + GI + TI + DI 8

C) SI + SP + SQ + SC + SL + SM 8

D) SI + SP + SQ + SC + SL + SM 8

Sub-question 4: Prof. Daves doesn't want to teach Mgt Science next semester. Which of the following accomodates his request? ____ ABCD____

A) DI + DP + DQ + DC + DL 3

B) SM + GM + TM + DM 1

C) DM = 0

D) DI + DP + DQ + DC + DL + DM 4

Sub-question 5: The department agrees to accomodate Prof. Saba's needs (minimum prep time) for his health issues. Which of the following best reflects this agreement? ____ ABCD____

A) SI + SP + SQ + SC + SL + SM 3

B) SI = 3, SI + SP + SQ + SC + SL+ SM = 3

C) SI + SP + SQ + SC + SL + SM 3

D) SI + SP + SQ + SC + SL + SM = 3