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STAT3800 Deterministic And Stochastic Optimisation

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STAT3800 Deterministic And Stochastic Optimisation

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Course Code: STAT3800
University: The University Of Newcastle

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Country: Australia

Question:
Describe about the Orientation and Indication and Extracurricular Activities.

Answer:
We have,
r3(0)=$0k r2(0)=$0k r1(0)=$0k
r3(1)=$2k r2(1)=$2k r1(0)=$2k
r3(2)=$3.4k r2(2)=$3.25k r1(2)=3.10k
r3(3)=$4.35k r2(3)=$4.35k r1(0)=$4.20k 
Now let gt(x) be an allocation of milk to store t that attains ft(x). Then:
f3(0)= r3(0)= 0.00k g3(0)=0
f3(1)= r3(1)= 2.00k g3(1)=1
f3(2)= r3(2)= 3.4k g3(0)=2
f3(3)= r3(3)= 4.35k g3(0)=3 
We need not compute f3(4), f3(5), and f3(6), because an optimal allocation will never have more than 3k litres to allocate to a single store (demand at any store is never more than 3 litres).
Therefore using backward recursion we get:
f2(0)= r2(0) + f3(0-0)=0 g2(0)=0
f2(1) = max{ r2(0) + f3(1-0)=2k , r2(1) + f3(1-1)=2k }        g2(1)=0 or 1 
f2(2) = max{ r2(0) + f3(2-0)=0+3.4=3.4k , r2(1) + f3(1-1)=2+2=4k, r2(2) + f3(2-2)=3.25+0 =3.25k  }        g2(2)=1 
f2(3) = max{ r2(0) + f3(3-0)=0+4.35=4.35k , r2(1) + f3(3-1)=2+3.40=5.4k,  r2(2) + f3(3-2)=3.25+2.0 =5.25k, r2(3) + f3(3-3)=4.35+0.0 =4.35k  }        g2(3)=1
Now in computing f2(4), f2(5) and f2(6), we need not consider any allocation for more than 3000 litres to store 2 or any that leaves more than 3000 litres for store 3
f2(4) = max{ r2(1) + f3(4-1)=2.0+4.35=6.35k , r2(2) + f3(4-2)=3.25+3.4=6.65k, r2(3) + f3(4-3)=4.35+2.00 =6.35k  }        g2(4)=2
f2(5) = max{ r2(2) + f3(5-2)=3.25+4.35= 7.6k , r2(3) + f3(5-3)=4.35+3.40=7.75k }        g2(5)=3
f2(6)= r2(3) + f3(6-3)=4.35+4.35=8.7 g2(6)=3And finally, we have
f1(6) = max{ r1(0) + f2(6-0)=0+8.70=8.7k , r1(1) + f2(6-1)=2.00+7.75=9.75k,  r1(2) + f2(6-2)=3.10+6.65 =9.75k, r1(3) + f2(6-3)=4.20+5.40 =9.60k  }        g1(6)=1 or 2
Thus we can allot 1k or 2k  litres to store 1. Let us suppose we arbitrarily choose to assign 1k litres to store1. Then we have 6-1 =5k litres for stores 2 and 3. Since f2(5) is attained by g2(5)=3, we assign 3k litres to store 2. Then 5-3=2k litres are available for store 3. Since g3(2)=2, we assign 2k litres to store 3. Although this policy obtains maximum expected revenue, f1(6)=$9.75k, the total revenue actually received on a given day may be more or less than $9.75k  
The question is like thisMaximise z=10x(1) + 3x(2) +7x(3)
2x(1)+3x(2)+2x(3)<=20 x(2)>=1
x(1)<=2 x(1), x(2), x(3)>=0
We must have x(2)<=6 because if we take x(2)=7, then we will have 3x(2) =21, i.e. greater than the length of the garden.Now we have to do cj/aj for all the variables:For x(1), cj/aj  = 10/2= 5 For x(2), cj/aj = 3/3 =1 For x(3), cj/aj = 7/2= 3.5 So firstly we take two x(1)s, then six x(3)s and then one x(2) Therefore, x(1)=2     x(2)=1     x(3)=6And, z= 10*2 + 3* 1 + 7*6=65 Free Membership to World's Largest Sample Bank To View this & another 50000+ free samples. Please put your valid email id. E-mail Yes, alert me for offers and important updates Submit  Download Sample Now Earn back the money you have spent on the downloaded sample by uploading a unique assignment/study material/research material you have. After we assess the authenticity of the uploaded content, you will get 100% money back in your wallet within 7 days. UploadUnique Document DocumentUnder Evaluation Get Moneyinto Your Wallet Total 2 pages PAY 2 USD TO DOWNLOAD *The content must not be available online or in our existing Database to qualify as unique. Cite This Work To export a reference to this article please select a referencing stye below: APA MLA Harvard OSCOLA Vancouver My Assignment Help. (2021). Deterministic And Stochastic Optimisation. Retrieved from https://myassignmenthelp.com/free-samples/stat3800-deterministic-and-stochastic-optimisation/expected-revenue.html. "Deterministic And Stochastic Optimisation." My Assignment Help, 2021, https://myassignmenthelp.com/free-samples/stat3800-deterministic-and-stochastic-optimisation/expected-revenue.html. My Assignment Help (2021) Deterministic And Stochastic Optimisation [Online]. Available from: https://myassignmenthelp.com/free-samples/stat3800-deterministic-and-stochastic-optimisation/expected-revenue.html[Accessed 18 December 2021]. My Assignment Help. 'Deterministic And Stochastic Optimisation' (My Assignment Help, 2021) accessed 18 December 2021.

My Assignment Help. Deterministic And Stochastic Optimisation [Internet]. My Assignment Help. 2021 [cited 18 December 2021]. Available from: https://myassignmenthelp.com/free-samples/stat3800-deterministic-and-stochastic-optimisation/expected-revenue.html.

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