1 of 3BUS 336 D100/D200 Data & Decisions IIAssignment #3 – Linear ProgrammingThis is an individual assignment. Identical papers will be given a mark of zero.Due date: Tuesday July 31st at 11:30am. Late papers will not be accepted.Please submit your assignment into your section’s drop box. The D200 (Surrey) drop box is located on the5th floor in Surrey at the top of the stairs. The D100 (Burnaby Day Section) is located on the 4th floor ofWMC. Please make sure to submit it into the correct drop box. Assignments submitted to the wrongdropbox will not be accepted. The box will be cleared immediately after the deadline and not checkedagain.Please feel free to use hand‐writing for this assignment, provided that it is neat. Marks will be deducted forunclear, disorganized or messy submissions. Please use the posted Assignment cover page. Please seepage 3 on this Assignment for instructions on pasting output from Excel into Word to meet the formattingrequirements.Question1: LP graphical analysis (you must use proper graph paper or you will lose marks)Hand in the following (Please try to limit your submission to no more than 3 pages – 1 page for your graphpaper and the second and third pages for your answers to parts a through e):Canadian Health Inc. processes health insurance claims for a large number of health insurancecompanies across Canada. The majority of claims being processed are completed by a large pool ofcomputer operators, some of whom are permanent employees and some are part‐time/flexibleemployees. On average, a permanent employee can process 18 claims per day whereas a part‐time/flexible employee can process 10 claims per day, and the company is required to process at least450 claims per day. The company is limited by 50 computer workstations for staff operators to processthe insurance claims (one operator per computer). A permanent employee generates about 0.6 claimswith errors each day, whereas a part‐time/flex employee averages about 1.5 defective claims per day.The company wants to limit the amount of errors to 45 per day. Furthermore, the company has decidedthat it requires a minimum of 10 part‐time/flex employees to be hired due to the seasonality influx ofclaims submitted throughout the year. A permanent employee is paid $145 per day and a part‐time/flexemployee is paid $79 per day. The company wants to determine the number of permanent and part‐time/flex operators to hire in order to minimize costs.Hand in the following (Please try to limit your submission to no more than 3 pages):a) Formulate the problem into “proper LP format” and solve graphically as shown in class using ONLYIsoprofit lines (level curves) (do not solve by evaluating all the extreme corners of the feasiblearea). Make sure to plot Permanent employees along the horizontal axis of your graph paper. Clearlyidentify on your graph the feasible area, the isoprofit lines and your optimal point or marks will belost! Clearly state the optimal solution in terms of the business problem. Be sure to state theminimized cost of the optimal solution.b) Using your answer in part a) solve algebraically for the two constraints involved in the optimalsolution. State your answer to the nearest 2 decimal places (despite the fact, there is no such thing asa fraction of a person!).c) What if the company increased the daily amount paid to part‐time/flex employees to $100 per day?Would the optimal solution change? Prove by graphing the new objective function and locating thenew optimal solution (if it exists). Clearly state the new optimal solution if there is a new optimalsolution. Again, state your answer to 2 decimal places.d) Suppose the company required that at least three times the amount of part‐time/flex employees areto be hired relative to permanent employees? Would the feasible area and the optimal solutionchange? Prove by graphing the new constraint and determine its impact on the original formulation.Clearly state the new optimal solution (if there is a new optimal solution).2 of 3e) Suppose the company is considering relaxing the defective error constraint (of the originalformulation) in order to further reduce costs. Should it do so? State why or why not. What is themaximum amount of defective claims per day that the company could allow before requiring therelaxation of other resource constraints?Question 2Donald Thump, an investment advisor for JP Dorkan, has $80,000 from a client to invest among severalinvestment options. The alternative investments being considered are an exchange‐traded fund (ETF)with an 8.5% annual return, Guaranteed Investment Certificates (GICs) with a 5% annual return,government bonds with a 3.5% annual return, and a stock index fund with a 13% annual return. Theinvestment will be evaluated after 1 year. The following are guidelines that Donald wants to use topromote diversity with the investment and lessen its risk:1. No more than 20% of the total investment should be placed in the exchange‐traded fund2. The amount invested in GICs should not exceed the amount invested in the other threealternatives3. At least 30% of the total investment should be placed in government bonds and GICs.4. In order to be conservative with his client’s funds, more should be invested in GICs andgovernment bonds than in ETFs and the stock index fund, by a ratio of at least 1.3 to 1.Using the information above, determine the optimal investment portfolio for Donald given that he wouldlike to maximize the total return of the investment for his client.a) Formulate the problem into proper LP format (do not assume that all $80,000 will be invested).b) Use Solver to determine the optimal solution. Generate both the Answer and Sensitivity Reports.c) Answer the following with respect to the LP reports generated in part b): i).ii).iii).What is the optimal solution in the context of the business problem?Interpret the meaningof the shadow price for the $80,000 max investmentInterpret the meaning of the reduced cost for ETFs. Hand‐in requirements for Question 2: Hand in the proper LP formulation and your answers to part c. Handin ONLY the “Answer and Sensitivity Report” for part b. (please try to put all onto 2 pages max). Do NOThand in ANY OTHER Excel output. Note: Parts b) and c) should be attempted after Week 11’s tutorial.Question 3 Please attempt this problem after Week 12’s tutorial.Humble Grocery chain operates in major cities across Canada. The store caters to patrons that desirefood products at low costs. For the majority of Humble’s food products, the company purchases itoverseas in high volumes allowing the company to sell food items at low prices. However for some fooditems, Humble Grocery purchases food products from other grocery stores just outside urban centersand ships it in. They can do this because of the higher prices that can be demanded within urban centersrelative to other locations. For example, Humble Grocery purchases baby food at stores in Abbotsford,Burnaby, Chilliwack, Surrey and Richmond and then trucks it to six stores in and around Vancouver. Thestores in the outlying areas know what Humble is up to, so they limit the number of cases of baby foodHumble can purchase. The following table shows the profit Humble makes per case of baby food, basedon where the company purchases it and at which store it is sold, plus the available baby food per week atpurchase locations and the shelf space available at each Humble Grocery store per week:Complete the following:a) Draw the transportation networkb) Formulate the problem into proper Linear programming format Humble Grocery Store Locations (SL) ‐ Profit/CasePurchase LocationSL1SL2SL3SL4SL5SL6SupplyAbbotsford$9$8$11$12$7$826Burnaby$10$10$8$6$9$740Chilliwack$8$6$6$5$7$420Surrey$4$6$9$5$8$1040Richmond$12$10$8$9$6$745Demand251530182735 3 of 3c) Use Solver to determine the optimal solution and state the optimal solution in the context of thebusiness problem.d) Suppose Humble can purchase all the baby food that it needs from a Vancouver Distributor at aprice that will result in a profit of $9 per case at stores 1, 3, and 4; $8 per case at stores 2 and 6;and $7 per case at store 5. Should Humble purchase all, none, or some of its baby food from thedistributor rather than purchase it at other stores and truck it in? Hint: To investigate thepossibility of purchasing “some” of the baby food from the Distributor, create an additional“Supply” node in your Excel Model to represent the Distributor!Hand‐in requirements for Question 3: Hand in the Transportation Network, the Proper LP formulation andyour answers to parts c and d. Hand in ONLY the “Answer and Sensitivity Report” for part c. (please try toput all onto 2‐3 pages max). Do NOT hand in ANY OTHER Excel output.Formatting for Assignment #3Please copy and paste your Answer and Sensitivity Reports from Excel to Word using the following method sothat it is properly formatted and legible.1. Highlight your Report with your mouse in Excel and select copy2. Open Word and select Paste (more arrow) and then Paste Special3. Select “Picture (Enhanced Metafile)” and press Okay.4. You will now be able to select the corner of the pasted picture (the Answer Report or SensitivityReport) and modify its size so that it is legible and clear to the reader.Happy formatting!
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