Need help with my Introduction to Management science homework problems

Problem 1 GPUs revisited : Unconstrained Optimization:

After you told your boss about the GPU problem I gave you for homework, they asked you to design a server blade that has 6 GPUs. They want these blades to be as powerful as possible. They heard that the company Nvidia sells GPUs for this purpose. They are the Titan series of GPUs. The GPU’s they are interested in and the associated costs are:

Titan RTX $2,500 Titan V CEO Edition $5,000 Titan V $3,000 Titan Xp $1,650 Titan X Pascal $1,250

Based upon the information on TechPowerUp’s web site:

Q1 What is the GPU to use if you need to maximize FP32 (Float) performance?

GPU to use:

Q2 How much does it cost for 6 of those? How much FP32 and FP64 performance do you get from 6 of those GPUs combined?

Total Cost:

Total FP32 performance:

Total FP64 performance:

Q3 What is the GPU you would use if you need to maximize FP64 (Double) performance? (Make sure to check your units!)

GPU to use:

Q4 How much does it cost for 6 of those from Q4? How much FP32 and FP64 performance do you get from 6 of those GPUs combined?

Total Cost:

Total FP32 performance:

Total FP64 performance:

Q5 Between the 2 sets of GPUs, those from Q1 and Q3:

What is the difference in FP32 performance?

What is the difference in FP64 performance?

What is the difference in cost?

If you will do most (80%) of your calculations using FP32 and 20% doing FP64, which set of GPUs would you choose and why?

Suppose that you heard about the GPGPUs another company makes. These GPGPUs tend to be cheaper and more powerful. They come from AMD and the model numbers and costs are:

AMD FirePro S9150 $300, Radeon Instinct MI25 $ 4,200 Radeon Instinct MI50 $ $8,000

The specs for the S9150 is available here. https://www.techpowerup.com/gpu-specs/firepro-s9150.c2608

Q6 What GPU will you select? What are the total costs, total FP32 and FP64 calculations?

GPU to use:

Total Cost:

Total FP32 performance:

Total FP64 performance:

Q7 Between the set of GPUs you suggested in Q5 and the GPU you select from Q6, which set would you choose and why?

All the GPGPUs above were really expensive, for the most part. None of them let you watch things on a screen. Consumer level GPUs can give you the ability to play video games and compute when not in use. Some of the best GPUs out right now for both computing and video gaming and cost are:

RTX 2080ti $1,100 RTX 2080 $800 GTX 1660 ti $ 270

Radeon RX5700 $ 400 Radeon VII $700 Vega 64 $400

Q8) Which GPU gives the best FP32?

Which GPU gives the best FP64?

Among the 6 gpus above, which one would you use and why? (Remember, you need to watch videos and compute.)

For the price, what is a better option, buying consumer grade GPUs or the best set of GPGPUs from earlier?

Problem 2 Multi-objective Optimization We have seen several problems that use Multi-objective optimization. Sometimes, it’s best to have multiple objective functions. Other times it is best to have one objective function and turn the other objective functions into constraints.

Q1 Suppose that you are in the situation where you have 2 or more objective functions and the optimal solution is NOT ACCEPTABLE. (i.e. minimizing cost => profits that are too low) or (Minimizing variability => to low returns) Describe how you would handle such a situation.

Q2 Suppose that you are in a situation where you have multiple objective functions and a solution does not exist. (example: You need 30hrs in the day to get everything done. But you only have 12.) Describe how you will handle that type of situation.

Problem 3 Distribution System Analysis Use and modify the Excel solver to solve the new problem given below. Assume that the objective function is shipping cost. (What do we want to do here?)

		Shipping costs per unit.
Plant		D1	D2	D3	D4
Clifton Springs		$35	$31	$32	$38
Dansville		$36	$30	$30	$40
Plant		Capacity		Customer Orders
Clifton Springs	8000		D1	4000
Dansville		5500		D2	7000
				D3	3000
				D4	2000

Q1) What is the new revenue (Objective Function Value) for the optimal solution and how much product goes to each distributor?

Objective Value	D1	D2	D3	D4

Q2) How much more product do you need to satisfy demand?

Q3) An accident occurred at the Dansville plant and it is now running at half capacity. What is your new cost and how much product do you send to each distributor?

Objective Value	D1	D2	D3	D4

Problem 4 Scheduling Problem

An issue that occurs within any academic department is that they need to schedule people based upon some set parameters. In this case, the department knows that they need to offer classes such that each full time professor teaches 3 classes per term and each part time professor teaches 1 or 2 classes. Suppose that there are 3 classes this department teaches. It’s is your job to assign classes to each professor based upon maximizing the quality of instruction in the department. The professor quality ratings are:

Prof	Class	Qual Score		Prof	Class	Qual Score
FT1	Class A	10		PT1	Class A	7
FT1	Class B	9		PT1	Class B
FT1	Class C	8		PT1	Class C	7
FT2	Class A	6		PT2	Class A	8
FT2	Class B	4		PT2	Class B
FT2	Class C	5		PT2	Class C	7
FT3	Class A	9		PT3	Class A
FT3	Class B	7		PT3	Class B	6
FT3	Class C	5		PT3	Class C	6

Q1) The department decides they will offer 4 sections of Class A, 3 sections of Class Band 2 sections of Class C. Who teaches what class(es) and how many sections do they teach? What does solver say about this situation?

Prof	Class	# Sections		Prof	Class	# Sections
FT1	Class A			PT1	Class A
FT1	Class B			PT1	Class B
FT1	Class C			PT1	Class C
FT2	Class A			PT2	Class A
FT2	Class B			PT2	Class B
FT2	Class C			PT2	Class C
FT2	Class D			PT2	Class D
FT3	Class A			PT3	Class A
FT3	Class B			PT3	Class B
FT3	Class C			PT3	Class C
FT3	Class D			PT3	Class D
QUALITY SCORE =>

Q2) The department realizes it’s mistake and decided to change the course offerings and now proposes 5 sections of Class A, 4 sections of Class B and 4 sections of Class C. Who teaches what class(es) and how many sections do they teach and what is the quality score?

Prof	Class	# Sections		Prof	Class	# Sections
FT1	Class A			PT1	Class A
FT1	Class B			PT1	Class B
FT1	Class C			PT1	Class C
FT2	Class A			PT2	Class A
FT2	Class B			PT2	Class B
FT2	Class C			PT2	Class C
FT2	Class D			PT2	Class D
FT3	Class A			PT3	Class A
FT3	Class B			PT3	Class B
FT3	Class C			PT3	Class C
FT3	Class D			PT3	Class D
QUALITY SCORE =>

Q3) Suppose that some of the full time profs decide that they don’t want to teach more than 2 sections of the same class. Does this restriction affect the optimal solution above?

Q4) Suppose that FT1 and FT3 don’t want to teach Class A. Who teaches what class(es) and how many sections do they teach and what is the quality score?

Prof	Class	# Sections		Prof	Class	# Sections
FT1	Class A			PT1	Class A
FT1	Class B			PT1	Class B
FT1	Class C			PT1	Class C
FT2	Class A			PT2	Class A
FT2	Class B			PT2	Class B
FT2	Class C			PT2	Class C
FT2	Class D			PT2	Class D
FT3	Class A			PT3	Class A
FT3	Class B			PT3	Class B
FT3	Class C			PT3	Class C
FT3	Class D			PT3	Class D
QUALITY SCORE =>

Problem 5 Where am I going to use this? the chapters that were discussed are Linear Programming, integer programming, non-linear programming, multiple objective programming and transportation and assignment

Q1) Thinking about all the things we discussed in this class, so far. Describe in 4-5 sentences where you could use the methods we discussed in 3 aspects of your personal life. (But not to personal. Keep it Rated G.)

Q2) Thinking about the material we discussed in this class, describe how you can use this material in your work life. Give 2 examples of 4-5 sentences each. (DO NOT DIVULGE ANY ILLEGAL ACTIVITIES!!!)

Problem 6 SHOW ME THE MONEY!!!!!!! Your job is to maximize the yield of someone’s stock portfolio. They want a minimum average return of 7% (0.07) to start. They have some concerns about variability too. Thou, initially, they are not that worried. You need to use the solver to answer the following questions.

Q1 What is the optimal mix of stocks to maximize returns and what is the return?

Return	A	B	C	D	E	F

Q2 How does setting the variability to 11% (0.11) affect the optimal mix and return?

Return	A	B	C	D	E	F

Q3 How does setting the variability to 7% (0.07) affect the optimal mix and return?

Return	A	B	C	D	E	F

Q4 Suppose that the client says they don’t want to have more than 50% (0.50) of their stock in any 1 company. How does affect the optimal mix and return if the maximum variability cannot exceed 7%?

Return	A	B	C	D	E	F

Q5 Of the 4 scenarios above, which would you choose and why? (2-3 sentences)

The customer came back and asked you to redo some of the calculations.

Q6 The customer wants a minimum return of 10% (0.10) and they do not want more than 50% of their stocks to be with one company. What are their stocks and what is their return?

Return	A	B	C	D	E	F

Q7 They asked you to rerun your solver when they want a minimum of 10% returns, variability to be under 3%(0.03) and no more than 50% of their stocks in any one company. What are their returns and what does the stock portfolio looking like?

Return	A	B	C	D	E	F

Q8 They asked you to rerun your solver when they want a minimum of 12% returns, variability to be under 3%(0.03) and no more than 25% of their stocks in any one company. If that is not possible, suggest a solution where you relax some of their constraints. Either way, what are their returns and what does the stock portfolio looking like?

Return	A	B	C	D	E	F

What is your min return? What is your Max variability? What are your constraints for portfolio allocation?