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      QBUS6820代做、Python編程語言代寫

      時間:2024-04-02  來源:合肥網hfw.cc  作者:hfw.cc 我要糾錯



      QBUS6820: Prescriptive Analytics Assignment 1 Semester 1, 2024
      Instructions: Submit your answers in one pdf document with each question/part labelled clearly. You
      must also submit your code - the raw code (.ipynb file) and a html version of your Jupyter Notebook.
      Problem 1: Investing (6 marks)
      Suppose a friend of yours wants to invest $10,000 and has asked for your help. They’re thinking of
      investing in an index fund tied to the ASX200 and a tech stock fund, but they’re concerned about
      the volatility of tech stocks. They therefore want to take measures to manage their investment risk.
      They’ve decided that the amount invested in the tech fund cannot be higher than twice the amount
      invested in the index fund. The price per share of the index fund is $17, and the price per share of
      the tech fund is $20. Over the last 5 years, the average annual return for the index fund has been
      15%, and 25% for the tech fund. They expect the performance of the funds in the coming year to be
      identical to the recent past. Your friend wants to develop an investment strategy that will maximise
      their return for the coming year.
      (a) Formulate a linear programming model to help determine how much money they should invest
      in each fund.
      (b) Solve the model using Python.
      (c) If your friend can get $1 more to invest, how will that affect the solution? $2 more? $3 more?
      What can you say about the return on their investment strategy given these changes.
      Problem 2: Producing wine (7 marks)
      A winery produces and sells three types of wine across Australia — No.1, No.2, and No.3. A few
      months ago management discovered a large number of grapevines in the vineyard were infested with
      an insect pest that feeds on their roots and eventually kills them. They had no choice but to take
      out all the grapevines and replant their crop. It will take years for the new vines to mature and
      produce grapes so in the meantime they must purchase grape juice from other vineyards to make
      their wine.
      There are three vineyards that are willing to sell their grape juice to the company - A, B, and C.
      They are located in different and faraway parts of the country. As such, the company is looking
      at using more conveniently located winemaking and bottling facilities instead of its own. It has
      identified 4 facilities: W, X, Y, and Z.
      In a particular month vineyard A can supply 1,500 tons of grape juice, vineyard B 1,600 tons, and
      vineyard C 1,000 tons. The processing capacity per month at facility W is 1,300 tons, 1,000 tons at
      X, 1,300 tons at Y, and 1,500 tons at Z. The $ cost per ton of transporting juice from the vineyards
      to the facilities is as follows:
      W X Y Z
      A 850 720 910 750
      B 970 7** 1,050 880
      C **0 830 780 820
      The processing facilities have different equipment and have different wage rates. The cost of processing each type of wine at each plant ($/ton) therefore differs, and is as follows:
      W X Y Z
      No.1 2,100 2,350 2,200 1,**0
      No.2 4,100 4,300 3,950 3,**0
      No.3 2,600 2,300 2,500 2,800
      This month the company needs to process a total of 1,400 tons of No.1, 800 tons of No.2, and 600
      tons of No.3 at the four facilities combined. There are two complicating factors though. To produce
      1 ton of No.2 requires 2 tons of grape juice, and 1 ton of No.3 requires 1.5 tons of grape juice. 1 ton
      of No.1 requires 1 ton of juice.
      The company wants to know how many tons of grape juice to ship from each of the vineyards to each
      of the facilities, and the number of tons of each type of wine to produce at each facility to minimise
      total costs.
      Page 1 of 2
      QBUS6820: Prescriptive Analytics Assignment 1 Semester 1, 2024
      Problem 3: Assigning groups (7 marks)
      Assume you’re a course coordinator assigning 15 students to 5 teams for a project. You want the
      project teams to be relatively equal in terms of academic performance and to have a mix of different
      skills and domestic/international students. You’ve decided to use students’ grade point average
      (GPA) as a proxy for academic performance and to set a minimum average GPA of 2.75 for each
      team while also maximising the overall average GPA across teams. You’ve also decided to use
      students’ majors as a proxy for different skill sets, but you don’t want there to be more than two of
      the same major in any single team. You also want at least one international student on each team,
      but not more than two. The following table details the GPA, major, and internationality of each
      student in the cohort.
      Student GPA International Major
      1 3.10 Yes FIN
      2 2.30 No ACCT
      3 2.31 Yes BA
      4 2.10 Yes MKTG
      5 3.28 No BA
      6 3.** No FIN
      7 2.92 No FIN
      8 2.60 No FIN
      9 3.17 No FIN
      10 3.03 Yes MKTG
      11 3.40 Yes MKTG
      12 2.** No ACCT
      13 2.66 Yes MKTG
      14 2.86 No ACCT
      15 3.40 Yes BA
      Formulate and solve an integer linear programming model for this problem to determine project
      teams that align with your criteria. Do you think your model does a decent job of making sure the
      teams are diverse and academically equitable? If not, how might you change your model to achieve
      a better result?
      Page 2 of 2

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