Please show work in putting information for each question in QM for Windows using Linear Programming to better understand how to calculate the answers for each question

	Undergrad	Graduate		RHS	Dual
Minimize	2500	3500
Undergrad Minimum	1	0	>=	30	0
Grad Minimum	0	1	>=	15	-1000
Contracts	1	1	>=	60	-2500
Solution	45	15		165000
Variable	Status	Value
Undergrad	Basic	45
Graduate	Basic	15
Surplus 1	Basic	15
Surplus 2	NONBasic	0
Surplus 3	NONBasic	0
Optimal Value (Z)		165000
Variable	Value	Reduced Cost	Original Val	Lower Bound	Upper Bound
Undergrad	45	0	2500	0	3500
Graduate	15	0	3500	2500	Infinity
Constraint	Dual Value	Slack/Surplus	Original Val	Lower Bound	Upper Bound
Undergrad Minimum	0	15	30	=-infinitiy	45
Grad Minimum	-1000	0	15	0	30
Contracts	-2500	0	60	45	Infinity

The dean of the western college of business must plan the schools course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 15 graduate courses in the term. Faculty contracts also dictate that at least 60 courses to be offered in total. Each undergraduate course taught costs an average of $2,500 in faculty wages, and each graduate course costs $3,500.

Use the table above from QM for Windows in order to formulate your answer:

1. The optimal solution requires teaching how many undergraduate courses?

1. 45
2. 30
3. 15
4. 60

2. The optimal solution would result in what surplus?

1. 15 undergraduate courses
2. 45 undergraduate courses
3. No surplus remains
4. 15 contracts

3. If the cost of graduate courses drop to $2,100, how would this impact the optimal solution?

1. That solution cannot be determined based on the tables provided
2. The course mix will shift to teaching fewer graduate courses
3. The course mix will stay the same
4. The course mix will shift something different than it was before

4. If the cost of graduate courses drops to $2800, what kind of model change would be required?

1. Changing constraint parameters
2. Adding constraints
3. Adding decision variables
4. Changing objective function coefficients
5. Changing constraint quantity values

5. If the dean decides to run the model in order to separate day and night courses, she can use the above ranging table to support her decision-making process.

1. True
2. False

6. If the AACSB requires new criteria involving an adjustment for summer courses, what kind of model change would be required?

1. Changing constraint parameters
2. Adding constraints
3. Adding decision variables
4. Changing object function coefficients
5. Changing constraint quantity values

7. If undergraduate minimum changes to 40, the dean can use the above ranging table to support her decision-making the process.

1. True
2. False

8. If undergraduate minimum changes to 40, how would this impact the optimal solution?

1. That solution cannot be determined based on the tables provided
2. The course mix will shift to teaching more graduate courses
3. The course mix will stay the same
4. The course mix will shift something different that it was before

9. If the cost of undergraduate courses increases to $2700, what kind of model change would be required?

1. Adding decision variables
2. Changing Constraint Parameters
3. Changing constraint quantity values
4. Adding Constraints
5. Changing objective function coefficients

10. If the cost of undergraduate courses increases to $2700, she can use the above ranging table to support her decision-making the process.

1. True
2. False