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The maximization of FP32 performance is based on the associated costs and the best GPU to use the process is Titan V CEO Edition $5,000.
Q2 (6pts) How much does it cost for 6 of those? How much FP32 and FP64 performance do you get from 6 of those GPUs combined?
minimize f(x)
subject to g_i (x)≤0 , i=1,.......m
h_i (x)=0 . i =1………p
The unconstrained optimization becomes
x ϵ R^n
The function is becoming feasible for the singular focus
low value of f(x)
f (x)= a^t x + b
Total Cost:
Total cost = 2,500 +5,000 + 3,000 + 1,650 + 1,250
total cost = 13400
Total FP32 performance:
f(x) = 2,500x_1 +5,000x_2 + 3,000x_3 + 1,650x_4 + 1,250x_5
Total FP64 performance:
maximum f(x)
subject to g_i (x)≥ 0 , i=1,.......m
h_i (x)=0 . i =1………p
The unconstrained optimization becomes
x ϵ R^n
The function is becoming feasible for the singular focus
high value of f(x)
f (x)= a^t x + b
Q3 (2pts) What is the GPU you would use if you need to maximize FP64 (Double) performance? (Make sure to check your units!)
GPU to use:
Objective objective function value 19389
variables 1050 1060 1070
coefficients 2138 4375 6463
values 0 0 3
calculated set to
constraint 1 1 1 1 3 4 GPU
constraint 2 170 300 400 1200 1500 cost
constraint 3 75 120 150 450 1000 power
constraint 4 1 1 1 1 1
0 0 97
Q4 (6pts) 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?
Objective objective function value 18000
variables 1050 1060 1070
coefficients 2500 5000 3000
values 0 0 6
Auxiliary variables 0 0 1
calculated
constraint 1 1 1 1 6 GPU
constraint 2 2500 5000 3000 18000 cost
constraint 3 1 1 1 6 power
constraint 4 1 1 1 1
0 0 97
Total Cost:
18000
Total FP32 performance:
=6
Total FP64 performance:
=18000
Q5 (10pts) Between the 2 sets of GPUs, those from Q1 and Q3:
What is the difference in FP32 performance?
The performance of FP32 is increased in set 2 as compared to set 1.
What is the difference in FP64 performance?
Similar to FP 32, the performance of FP64 is increased in set 2 as compared to set 1.
What is the difference in cost?
initial cost =19389
final cost =18000
difference = 19389 - 18000
= 1389
If you will do most (80%) of your calculations using FP32 and 20% doing FP64, which set of GPUs would you choose and why?
Percentage differences
FP32 = 19389×0.8 = 15,511
FP 64 = 18000×0.2 = 3600
The 80% of calculation by using FP 32 is preferred as compared to the 20% of FP 64.
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 (8 pts) What GPU will you select? What are the total costs, total FP32 and FP64 calculations?
GPU to use: FP32
Total Cost: 38778
Total FP32 performance: 25200
Total FP64 performance: 25200
Objective objective function value 38778
variables 1050 1060 1070
coefficients 2138 4375 6463
values 0 0 6 calculated set to
constraint 1 1 1 1 3 4 GPU
constraint 2 9150 300 4200 25200 1500 cost
constraint 3 1 1 4200 25200 1000 power
constraint 4 1 1 1 1 1
0 0 97
Q7 (4pts) Between the set of GPUs you suggested in Q5 and the GPU you select from Q6, which set would you choose and why?
On the basis of conclusion in Q5 and the GPU of Q6 the set will be more better. The calculated cost in both cases is different.
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 (12 pts)
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?
Objective objective function value 1620
variables 1050 1060 1070
coefficients 2080 800 270
values 0 0 6 calculated
constraint 1 1 1 1 6
constraint 2 1100 800 270 1620
constraint 3 400 700 400 2400
Problem 2 Multi-objective Optimization (25 points):
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 (13 pts) 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.
The process to handle the situation is based on the multiple objective programming. The frequent analysis is based on the optimization of problem with the set of objectives and it is often consistent with each other.
Multiple objective LP is on the LP of the form
max〖 z 〗 = {c^1 x_6 c^2 x …….c^r x}
MP = Ax≤ b
x≥ 0
In the equation {c^1,c^2 …….c^r } is the set of r-objective vectors, expect the limited circumstances.
Q2 (12 pts) 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.
On the basis of information, it is not possible to find out the solution that is not available simultaneously to maximize all of the objectives.
Problem 3 Distribution System Analysis (25 points):
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) (10pts) What is the new revenue (Objective Function Value) for the optimal solution and how much product goes to each distributor?
New revenue
Shipping costs per unit.
Plant D1 D2 D3 D4 capacity
Clifton Springs $35 $31 $32 $38 $8,000
Dansville $36 $30 $30 $40 $5,500
Demand 4000 7000 3000 2000
Plant D1 D2 D3 D4 capacity
Clifton Springs $1,000 $2,000 $3,000 $0 $6,000
Dansville $2,000 $0 $0 $2,000 $4,000
Demand $3,000 $2,000 $3,000 $2,000
How much product goes to each distributor?
D1 = 3000
D2 = 2000
D3 = 3000
D4 = 2000
Q2) (5 pts) How much more product do you need to satisfy demand?
Total demand = 4000 + 7000+ 3000+2000
total demand =16,000
Total capacity = 8000+5500
total capacity =13,500
difference = 16000 - 13500 = 2500
Therefore, it can be concluded that we need 2500 units so we can satisfy the demand.
Q4) (10 pts) 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?
Shipping costs per unit.
Plant D1 D2 D3 D4 capacity
Clifton Springs $35 $31 $32 $38 $8,000
Dansville $36 $30 $30 $40 $5,500
Demand 4000 7000 3000 2000
Plant D1 D2 D3 D4 capacity
Clifton Springs $3,000 $0 $3,000 $0 $6,000
Dansville $0 $0 $0 $2,000 $2,000
Demand $3,000 $0 $3,000 $2,000
Total Revenue 281000
total revenue = $281,000
Problem 4 Scheduling Problem (25 points):
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) (5 pts) 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?
The code of the question
#in clude <studio.h>
Void main()
Char names [20] high name [20] low name [20];
In score high low higest [4] lowest [4];
Float aver [4]
Int ij;
For [int i = 0; i < 4; i++]
{
Printf (“class:% d “, i);
Int sum = 0;
For (j=0; j<5; j++)
{
Printf (“enter name:”);
Scanf (“%s”, Names);
printf (“Enter score:”);
scanf(“%d”, & score);
If (j==0)
Strcpy (high name, name);
Strcpy (low name, names);
High = score;
Low = score;
}
else
{
If(score>high)
{high = score;
Strcpy(high name, Names);
}
If (score< low)
{
low = score;
strcpy(lowname, names);
}
}
Q2) (5pts) 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?
Sum = sum + score;
}
Highest [i] = high;
Lowest [i] = low;
Avera [i] = (float) sum/5;
}
Floa high avg = average [0];
Int high all = highest [0], h = 0, low =0;
Printf (“Average for each class”);
Printf (“class; 1\f% f”, averga[0]);
Float avg avg = averg [0];
For (int I = 1; i<4; i++)
{avgavg = avera[i];
If (highest [i]> highall)
{
h=I, highall = highest [i];
}
If (avera [i] > highavg)
{
Highavg = avera[i]; hav =I;
}
If ( avera[i]> highavg)
{ highavg = avera [i];}
Printf (“Class:% d\t%f”, i+1, avera[0]);
}
Printf (“Average across all classes: %f”, avg avg/4”);
Printf (“Highest student score in each class”);
Q3) (5pts) 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?
For
(
int i=0; i<4; i++
)
Avgavg = avera [i];
If (highest [i] > highall)
{
High avg = avera[i]; hav=I;
}
Printf (“class:%d\t%f”, i+1, avera[0]);
}
Printf (“Average across all classes%f”, avgavg/4);
Printf(“Highest student score in each class”);
For (int i=0; i<4; i++)
Printf (“class1:%d\t%d”, i+1, highest[i]);
Printf (“highest class average % f.”, high avg);
Getch();
}
Q4) (10pts) 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 10 PT1 Class A 10
FT1 Class B 9 PT1 Class B 9
FT1 Class C 8 PT1 Class C 8
FT2 Class A 6 PT2 Class A 6
FT2 Class B 4 PT2 Class B 4
FT2 Class C 5 PT2 Class C 5
FT2 Class D 9 PT2 Class D 9
FT3 Class A 7 PT3 Class A 7
FT3 Class B 5 PT3 Class B 5
FT3 Class C 10 PT3 Class C 10
FT3 Class D 9 PT3 Class D 9
QUALITY SCORE => 8
Problem 5 Where am I going to use this? (25 pts)
Q1) (15 pts) 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.)
The major goal of the analysis was to explore the knowledge that was required to measure the learning outcomes. The research questions were about the science and mathematical process. The primary source of information is textbook with the examples. The course work measure quality score and classes.
Q2) (10 pts) 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!!! DO NOT DIVULGE ANY COMPANY SECRETS!!!)
The course work is related to optimization of solutions, constraint analysis, and measurement of capacity of distributors. The questions are used to measure the product and to satisfy the demand of products. Some questions are related to distribution system analysis and multiple objective functions and to define the existence of solution.
Problem 6 SHOW ME THE MONEY!!!!!!! (50 pts)
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 (5pts) What is the optimal mix of stocks to maximize returns and what is the return?
Return A B C D E F
Q2 (5 pts) How does setting the variability to 11% (0.11) affect the optimal mix and return?
Return A B C D E F
1 10 1 1 0 1
Q3 (5 pts) How does setting the variability to 7% (0.07) affect the optimal mix and return?
Return A B C D E F
1 8 0 1 1 1
Q4 (5 pts) 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
1 9 1 1 1 0
Q5 (5 pts) Of the 4 scenarios above, which would you choose and why? (2-3 sentences)
The analysis shows that the maximized objective is equal to 103. The customer came back and asked you to redo some of the calculations. The results show difference in the stock values of 7% and 50%. The report define that the outcomes of report affect the optimal mix and the maximum variability cannot exceed 7%.
Q6 (5 pts) 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
1 5 1 1 0 1 0
Q7 (5 pts) 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
1 4 1 0 1 1
Q8 (15 pts) 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
1 6 6 1 1 1
Objective Maximize 103
FT11A FT1B FT1C FT2A FT2B FT2C FT3A FT3B FT3C PT1A PT1C PT2A PT2C PT3B PT3C
Values 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Coeff 10 10 8 9 7 5 9 5 7 4 7 8 2 6 6
Calc Set to
FT Prof 1 1 1 1 3 3
FT Prof 2 1 1 1 3 3
FT Prof 3 1 1 1 3 3
PT Prof 1 1 1 2 1
PT Prof 2 1 1 2 1
PT Prof 3 1 1 2 1
Class A 1 1 1 1 1 5 2
Class B 1 1 1 1 4 3
Class C 1 1 1 1 1 1 6 5
What is your min return?
Calc Set to
3 3
3 3
3 3
What is your Max variability?
Calc Set to
2 1
2 1
2 1
What are your constraints for portfolio allocation?
Calc Set to
3 3
3 3
3 3
2 1
2 1
2 1
5 2
4 3
6 5
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