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**Question No. 1 **

The key to successfully complete the assignment is to define the variables and to develop the constraints to meet the conditions specified in the case study.

**Question No. 2 **

Most adults say they would prefer to die at home. The minority actually does, but the trend is moving toward death in the home rather than the hospital. What do you think of the trend?

**Question No.3 **

This week we are being taught Linear Programing which is a tool used to Maximize or minimize the solution with minimal resources. While reviewing this week's forum it really got me thinking about the real-world application of this model and how we essentially use it in management on a weekly or bi monthly basis if we simply are discussing the scheduling benefits side of the example. When I would create the schedule, I generally had a good idea when the heavy traffic times were and what the least amount of foot traffic occurs. I had a set hour I could use per pay period and had to schedule accordingly. I need to mention that it was highly frowned upon to have any sort of overtime. Scheduling would get tricky when holidays came around because we would be given extra hours but no where near the amount needed to cover the shift. At the time I did not know there wasn't a model available to tell me how to optimize my coverage while utilizing the fewest hours.

Watching the video made more sense than the case study because in my opinion there was one right answer. How can you maximize your profit with the resources you had available? There was a set number of parts used to make each model car and a set profit amount for each separate model. The Model was a linear model and needed no non-negative constraints. Best solution showed making 14 Deluxe, 6 Normal, 5 Orange, and 0 Grey with a profit of $1,090. Even showed the slack left over. With the Case study we are having issues with the two different Over time options as well as the percentage of part time employee's vs full time employees. I am still working with my team on the case study to understand and be able to speak on it more but I can tell you the video was 100% more understandable. I knew exactly what the constraints were and what my objective was. All I had to do was plug and go and get the answer needed.

**Question No. 4 **

For the case study assignment, I feel I have a workable grasp of the concepts for Linear Progression, however, in conducting the assignment I feel that I am short on my constraints. Regarding the Help File, it states that we should have 22 constraints in total, I am only able to come up with 19, and am not sure if they 100 percent accurate. My Constraints are as follows:

9-10 am

10-11am

11-12am

12-1 am

1-2 am

2-3 am

3-4 am

4-5 am

5-6 am

6-7 am

OT (from the Chase bank example I used 2OT1 +2OT2-2F<= 0)

PT @40%

PT Employees leaving at 1pm

PT Employees leaving at 2pm

PT Employees leaving at 3pm

PT Employees leaving at 4pm

PT Employees leaving at 5pm

PT Employees leaving at 6pm

PT Employees leaving at 7pm

This puts me at 19 constraints vice the 22. I'm just wondering what I am missing here to make up the other two constraints. Also, for the Q values ( I figure that is where we account for 4-7 hours of part time work), I put the Q value at costing -$7.82 or exactly the opposite of a part time hourly rate. Is this accurate? I do not believe the number I have when I solve is optimal due to the fact that there is too much surplus hours. Looking at the Chase example, I feel their answer is limited by assuming only 4 hour shifts. That being said, I feel my answer should not be too far off theirs as the constraints in terms of max PT employee hours are the same, yet my answer is far larger than what they have derived.

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**Answer No. 1**

It is the foremost per the step that would help in considering the steps under which solving the related of the linear programming problem. This would be adequately be defined under the decision variables that can be made as a part of the want and the determination with respect to the problem. Understanding the constraint needs to be related to the prelim condition such as the optimization problem. Under this, the solution needs to consequently be satisfied with respect to the equalities or inequalities. The constraint that which would consider under the framework of the selected ways per the optimal solution that would be able to provide the best feasible region. It would be solving an LPP, that can be related to the segregate as a part of the possible constraints which would be explaining the maximization of the number of iterations along with the computational effort. IThis would be working under the system of the large scale LP problems along with the relatively small percentage and need to work per the constraints that can also be binding at the optimal solutions.

**Answer No. 2**

This is also one of the parameters that would be related to the countries. It is also related to the proportion that can be related to the people dying with respect to the hospital and this be under the decreasing for years. Under the people would also relate to the want and with the framework of the last hours with respect to the home. This would not be made as per the hospital, that would be considered under the case. As such the trend reversal needs to be initiated, under the study that is related to the Max Planck Institute for Demographic Research (MPIDR) with respect to the Rostock shows. It would need to be understood per the proportion of elderly people that would be dying within the clinic that has been consequently been declining for years.

**Answers No.3**

This week we are being taught Linear Programming which is a tool used to Maximize or minimize the solution with minimal resources. While reviewing this week's forum it really got me thinking about the real-world application of this model and how we essentially use it in management on a weekly or bi-monthly basis if we simply are discussing the scheduling benefits side of the example. When I would create the schedule, I generally had a good idea when the heavy traffic times were and what the least amount of foot traffic occurs. I had a set hour I could use per pay period and had to schedule accordingly. I need to mention that it was highly frowned upon to have any sort of overtime. Scheduling would get tricky when holidays came around because we would be given extra hours but nowhere near the amount needed to cover the shift. At the time I did not know there wasn't a model available to tell me how to optimize my coverage while utilizing the fewest hours.

Watching the video made more sense than the case study because in my opinion there was one right answer. How can you maximize your profit with the resources you had available? There was a set number of parts used to make each model car and a set profit amount for each separate model. The Model was a linear model and needed no non-negative constraints. Best solution showed making 14 Deluxe, 6 Normal, 5 Orange, and 0 Grey with a profit of $1,090. Even showed the slack left over. With the Case study, we are having issues with the two different Overtime options as well as the percentage of part-time employees as full-time employees. I am still working with my team on the case study to understand and be able to speak on it more but I can tell you the video was 100% more understandable. I knew exactly what the constraints were and what my objective was. All I had to do was plug and go and get the answer needed.

Under the linear optimization system, it is of the process it would be considered as a part of the certain linear relationships that would help in the attainment of the possible solution related to the mathematical model. This would also channelize under the problems that would be dealing as per the maximizing profits along with the trends of the minimizing costs and as per the minimal usage with respect to the resources, etc. As such the problems that would relate to the linear programming problems (LPP). As such the strategies need to be uniformly utilized per the device that can be contributed to the maximum as a profit that can also be allocated with respect to the different amount of labor force which can be applied per the two types of cabinets. under this system, there needs to be a work with LPP that can help to find out a strategy that would be perspective per the leading perspective of the maximum profit. Under this, there were also the two sifts one that would be related to the less traffic and also under the system of the more traffic that can help in the crawling heavy pay to less with respect to the more. As such the percentage of part-time employees would be less and also be respective full-time employees.

**Answer No. 4 **

For the case study assignment, I feel I have a workable grasp of the concepts for Linear Progression, however, in conducting the assignment I feel that I am short on my constraints. Regarding the Help File, it states that we should have 22 constraints in total, I am only able to come up with 19, and am not sure if they 100 percent is accurate. My Constraints are as follows:

1) 9-10 am

2) 10-11am

3) 11-12am

4) 12-1 am

5) 1-2 am

6) 2-3 am

7) 3-4 am

8) 4-5 am

9) 5-6 am

10) 6-7 am

11) OT (from the Chase bank example I used 2OT1 +2OT2-2F<= 0)

12) PT @40%

13) PT Employees leaving at 1 pm

14) PT Employees leaving at 2 pm

15) PT Employees leaving at 3 pm

16) PT Employees leaving at 4 pm

17) PT Employees leaving at 5 pm

18) PT Employees leaving at 6 pm

19) PT Employees leaving at 7 pm

This puts me at 19 constraints vice the 22. I'm just wondering what I am missing here to make up the other two constraints. Also, for the Q values ( I figure that is where we account for 4-7 hours of part-time work), I put the Q value at a cost -$7.82 or exactly the opposite of a part-time hourly rate. Is this accurate? I do not believe the number I have when I solve is optimal due to the fact that there are too much surplus hours. Looking at the Chase example, I feel their answer is limited by assuming only 4-hour shifts. That being said, I feel my answer should not be too far off theirs as the constraints in terms of max PT employee hours are the same, yet my answer is far larger than what they have derived.

As such the problem should be worked under the parameters of the 19 constraints also. It needs to be under the q-value which is analyzed to be accurate having a costing of the -$7.82. As such the equality constraints should e there. There is also one of the slack variables related to the surplus variables. As such the constraints should also be under the less than the fixed number that could be relevant to the type of equations and it would be determined as an undetermined. Under this, there would be an unknown system of the linear programming problem that can be measured through the degree of freedom. Also, the equation would be made part of the system perceived under the constraint under which it would restrict one degree of freedom. hence the critical case (such as the overdetermined along with the underdetermined) would happen over the number of equations along with the number of free variables that are equal. It is important that every variable would also provide a degree of freedom which would be part of the constraint that is part of the degree of freedom.

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