Question

Choose the best set of GPUs to maximize my ability to compute. I've done some research and looked into something called GPGPU (General Purpose Graphical Processing Unit). I have my eyes a few of these more powerful GPGPUs. They are and cost: GPUS RX580 RX590 Vega 56 Vega 64 Radeon VII Price $180 $210 $300 $400 $650 RAM8GB 8GB 8GB 8GB 16GB Suppose that I want to maximize my Double Float Point calcs. Look up these GPGPUs on TechPowerUp's GPU data base. Initially, assume that I can have 4 GPU total and I have 1,250W to spare. Enter that data into the GPU spread sheet and answer the following Q1 (5 pts) What GPUs and how many do I buy when my budget is $1,500? RX580 RX590 Vega 56 Vega 64 Radeon VII GPU Count Q2 (5 pts) What GPU and how many do I buy when my budget is $1,000 GPU RX580 RX590 Vega 56 Vega 64 Radeon VI Count Q3 (10 pts) Assuming a $1,000 budget, what happens when I find a "Flash Sale" and find the GPUs are now on sale for 25% off? GPU RX580 RX590 Vega 56 Vega 64 Radeon VII Count Q4 (10 pts) Suppose that I find out that I need to have at least 32GB of ram to fit the models I want to run. What do I buy now? RX580 RX590 Vega 56 Vega 64 Radeon VII GPU Count Q5 (20pts) Suppose that I need to maximize the ram I can get to fit my models. And I want to maximize the amount processing power I can get, and I find a way to use a larger number of GPUs. Say 20. Without solving this problem, describe in a paragraph or two what issues I might encounter and how I might need to sole it using methods we covered in class. Double float from website Vega 64: 7864 Randeon VII: 3360 RX580: 3859 RX590: 4450 Vega 56: 6604

Answer 1

Let

X1 = 1, if GPU RX580 is to be bought, otherwise X1 = 0

X2 = 1, if GPU RX590 is to be bought, otherwise X2 = 0

X3 = 1, if GPU Vega 56 is to be bought, otherwise X3 = 0

X4 = 1, if GPU Vega 64 is to be bought, otherwise X4 = 0

X5 = 1, if GPU Radeon VII is to be bought, otherwise X5 = 0

N1 = number of GPU RX580 to be bought

N2 = number of GPU RX590 to be bought

N3 = number of GPU Vega 56 to be bought

N4 = number of GPU Vega 64 to be bought

N5 = number of GPU Radeon VII to be bought

Q1) Linear program is following:

Max 3859N1+4450N2+6604N3+7864N4+3360N5

s.t.

X1+X2+X3+X4+X5<=4

180N1+210N2+300N3+400N4+650N5 <= 1500

10X1-N1 >= 0,  (here, 10 is just a hypothetical large number, larger than the maximum possible value of Ni)

10X2-N2 >= 0

10X3-N3 >= 0

10X4-N4 >= 0

10X5-N5 >= 0

Xi binary,

Ni >= 0

Solution using LINGO is following:

Lingo 170-Solution Report . Lingo! File Edit Solver Window Help Solution Report-Lingo1 Lindo Model- Lingo1 Global optimal solution found Max 3859N1+4450N2+6604N3+7864N4+3360N5 Objective value: 33020.00 Objective bound: 33020.00 Infeasibilities: 0.000000 S.t Extended solver steps: Total solver iterations: Elapsed runtime seconds: 0.40 180N1+210N2+300N3+400N4+650N5 1500 <= Model Class: MILP 10 Total variables: 1022-N2 0 >= Nonlinear variables: Integer variables: 10X3-N3-0 Total constraintS: 10X4-N4 -0 Nonlinear constraints: 25 Total nonzeros: Nonlinear nonzeros: END INT X1 Value INT X Variable Reduced Cost INT X3 N1 0.000000 103.4000 INT X4 N2 0.000000 172.8000 INT X5 N3 5.000000 0.000000 N4 0.000000 941.3333 N5 0.000000 10948.67 Xi 0.000000 0.000000 X2 0.000000 0.000000 X3 1.000000 0.000000 X4 0.000000 0.000000 x5 0.000000 0.000000 Row Slack or Surplus 33020.00 Dual Price 1.000000 1 3.000000 0.000000 0.000000 22.01333 0.000000 0.000000 For Help, press F1 CAP NUM

N1 = 0

N2 = 0

N3 = 5

N4 = 0

N5 = 0

GPU	RX580	RX590	Vega 56	Vega 64	Radeon VII
Count	0	0	5	0	0

Q2)

Revised model and solution is following:

Lingo 17.0-Solution Report-Lingo! File Edit Solver Window Help Solution Report-Lingo1 Lindo Model-Lingo Global optimal solution found Max 3859N1+4450N2+6604N3+7864N4+336ONS Objective value: Objective bound: 21517.00 21517.00 Infeasibilities: 0.000000 s.t. Extended solver steps: X1 +X2+X3+X4+X5<-4 Total solver iterations: Elapsed runtime seconds: 0.15 180N1+210N2 +300N3+400N4+650N5 1000 <= Model Class: PILP 10X1-N0 10 Total variables: 10X2-N2 0 Nonlinear variables: >= Integer variables: 10 Total constraints: 10X4-N4 0 Nonlinear constraints: >= Total nonzeros: 25 Nonlinear nonzeros: END INT X1 | Variable INT X2 Value Reduced Cost INT X3 Ni 1.000000 -3859.000 INT X4 N2 1 . 000000 -4450.000 INT X5 N3 2.000000 -6604.000 GIN NI N4 0.000000 -7864.000 GIN N2 NS 0.000000 -3360.000 GIN N3 x1 1.000000 0.000000 GIN N4 1.000000 0.000000 X2 GIN NS X3 1.000000 0.000000 X4 0.000000 0.000000 X5 0.000000 0.000000 Row Slack or Surplus Dual Price 21517.00 1.000000 1.000000 0.000000 10.00000 0.000000 9.000000 0.000000 For Help, press F1 CAP NUM

N1 = 1

N2 = 1

N3 = 2

N4 = 0

N5 = 0

GPU	RX580	RX590	Vega 56	Vega 64	Radeon VII
Count	1	1	2	0	0

Q3) The revised model and solution is following:

Unit Cost is multiplied with 0.75 to account for 25% off on price

翌Lingo 17.0-Solution Report-Lingo! File Edit Solver Window Help | [ | s, | F Solution Report . Lingo! Lindo Model-Lingo Global optimal solution found Objective value: Max 3859N14450N2+6604N3+7864N4+3360NS 28712.00 Objective bound: 28712.00 Infeasibilities: 0.000000 Extended solver steps: X1+X2+X3+X4+X5<-4 Total solver iterations: Elapsed runtime seconds: 0.12 135N1157.5N2+225N3+300N4+487.5N5 <-1000 Model Class: PILP Total variables: 10 10X2-X2 0 Nonlinear variables: >= 10 Integer variables: 10X3-N30 Total constraints: 10X4-X4 0 Nonlinear constraints: >= 25 10X5-NS0 Total nonzeros: Nonlinear nonzeros: END INT X1 Variable INT X2 Reduced Cost Value INT X3 N1 0.000000 -3859.000 INT X4 N2 2.000000 -4450.000 INT X5 N3 3.000000 -6604.000 GIN N1 N4 0.000000 -7864.000 GIN N2 N5 0.000000 -3360.000 GIN N3 0.000000 0.000000 X1 GIN N4 X2 1 . 000000 0.000000 GIN N5 X3 1.000000 0.000000 X4 0.000000 0.000000 X5 1.000000 0.000000 Row Slack or Surplus 28712.00 Dual Price 1.000000 1.000000 0.000000 10.00000 0.000000 0.000000 0.000000 For Help, press F1 NUM

GPU	RX580	RX590	Vega 56	Vega 64	Radeon VII
Count	0	2	3	0	0

Q4)

Additional constraint for RAM space is added to the model. Revised model and its solution is following:

翌Lingo 17.0-Solution Report-Lingo! Eile Edit Solver Window Help -11回11 x 'solution Report-Lingo! Lindo Model Lingo1 Global optimal solution found Objective value: Objective bound: Max 3859N1+4450N2+6604N3+7864N4+3360N5 21517.00 21517.00 Infeasibilities: 0.000000 S.t Extended solver steps: X1+X2+X3+X4+X5- Total solver iterations: 0.14 Elapsed runtime seconds: 180N1+210N2+300N3+400N4+65ONS 1000 Model Class: PILP 8N1+8N2+8N3+8N4+16N5 32 <= Total variables: 10 10X1-N0 Nonlinear variables: Integer variables: 10 10X2-N20 Total constraints: 10X3-N3-0 Nonlinear constraints: 0 Total nonzeros: 30 Nonlinear nonzeros: 0 10X5-NS0 END Value Variable Reduced Cost INT X1 N1 1.000000 -3859.000 INT X2 N2 1.000000 4450.000 -6604.000 N3 2.000000 INT X3 INT X4 N4 0.000000 7864.000 -3360.000 INT X5 NS 0.000000 GIN N X1 1.000000 0.000000 GIN N2 X2 1.000000 0.000000 GIN N3 X3 1 . 000 000 0.000000 GIN N4 0.000000 0.000000 GIN N 0.000000 X5 0.000000 Row Slack or Surplus 21517.00 Dual Price 1 1.000000 1.000000 0.000000 10.00000 0.000000 0.000000 0.000000 For Help, press F1 CAP NUM

GPU	RX580	RX590	Vega 56	Vega 64	Radeon VII
Count	1	1	2	0	0