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Homework answers / question archive / Part I- Discussion question (Clearly discuss the following terms) A Total of 4 Points 1

Part I- Discussion question (Clearly discuss the following terms) A Total of 4 Points 1. What are the basic differences between CPM and PERT? 2 Points 2. Explain the difference between forward pass method and backward pass method? 1 Point 3. What is the difference between pure strategy and mixed strategy games? 1 Point Part II- Work out (show all the necessary steps) A Total of 46 Points 1. An individual is in the process of buying a car and has narrowed the choices to three models, M1, M2, and M3. The deciding factors include purchase price (PP), maintenance cost (MC), cost of city driving (CD), and cost of rural driving (RD). The following table provides the relevant data for 3 years of operation. Use the profit data to develop the comparison matrices. Assess the consistency of the matrices, and determine the choice of model. Car Model Decision alternatives PP ($) MC ($) CD ($) RD ($) M1 $ 6,000 $1,800 $4,500 $1,500 M2 $ 8,000 $ 1,200 $ 2,250 $750 M2 $ 10,000 $ 600 $ 1,125 $600 • ? = 0.6 Based on the above information answer the following Questions? A. What is the value of the decision based on the Hurwicz criteria? 2 Points B. What is the value of the decision based on the Laplace criterion? 2 Points C. What is the value of the decision based on the Maxi-min criterion? 1 Point D. What is the value of the decision based on the Mini-max regret (Savage) criterion? 1 Point 2. The three blood banks in Addis Ababa City are coordinated through a central office that facilitates blood delivery to four hospitals in the city. The cost to ship a standard container of blood from each bank to each hospital is shown in the table below. Also given are the weekly number of containers available at each bank and the weekly number of containers of blood needed at each hospital. How many shipments should be made weekly from each blood bank to each hospital. Based on the information given under the table; A. Calculate the initial feasible solution by using LCM? 1 Point B. Find the optimal solution by using the stepping stone method and compare the result with the above method? 4 Points 3. On their farm, the Friendly family grows apples that they harvest each fall and make into three products apple butter, applesauce, and apple jelly. They sell these three items at several local grocery stores, at craft fairs in the region, and at their own Friendly Farm Pumpkin Festival for 2 weeks in October. Their three primary resources are cooking time in their kitchen, their own labor time, and the apples. They have a total of 500 cooking hours available, and it requires 3.5 hours to cook a 10-gallon batch of apple butter, 5.2 hours to cook 10 gallons of applesauce, and 2.8 hours to cook 10 gallons of jelly. A 10-gallon batch of apple butter requires 1.2 hours of labor, a batch of sauce takes 0.8 hour, and a batch of jelly requires 1.5 hours. The Friendly family has 240 hours of labor available during the fall. They produce about 6,500 apples each fall. A batch of apple butter requires 40 apples, a 10-gallon batch of applesauce requires 55 apples, and a batch of jelly requires 20 apples. After the products are canned, a batch of apple butter will generate $190 in sales revenue, a batch of applesauce will generate a sales revenue of $170, and a batch of jelly will generate sales revenue of $155. The Friendlys want to know how many batches of apple butter, applesauce, and apple jelly to produce in order to maximize their revenues. A. Formulate a linear programming model for this problem (develop in a table and write it in LPP form)? 2 points B. Solve the problem by using the simplex method (change into standardization form, find the initial feasible solution, find the optimal solution and interpret the result)? 5 points 4. Maraton Motors has four machines used to offer mechanical service to its customers and the company has four operators which are going to assigned in to these four machines. As an MBA student please advise the company for the optimal assignment by computing total minimum cost. Identify all alternative solutions if there are multiple optimal solutions? (3 Points) 5. Two Companies, A and B, sell two brands of paper. Company A advertise in radio (A1), television (A2), and newspaper (A3). Company B, in addition use radio (B1), television (B2), and newspapers (B3), also mails broachers (B4). Depending on the effectiveness of each advertising campaign, one company can capture a portion of the market from the other. The following matrix summarizes the percentage of the market captured or lost by company A. B1 B2 B3 B4 A1 8 -2 9 -3 A2 6 5 6 8 A3 -2 4 -9 5 A. What is the saddle point for the game? 1 Point 6. Brothers Biscuit and flour manufacturing Company is in the process of preparing a budget for launching a new product. The following table provides the associated activities and their durations are given in the next table. Activity Predecessor (s) Duration (Weeks) A: Forecast Sales volume Start 5 B: Study competitive market A 4 C: Design item and facilities B 6 D: Prepare production schedule B 2 E: Estimate cost of production C 7 F: Set sales price C,D 1 G: Prepare Budget E,F 5 A. Draw the network diagram for the above table? 1 Point B. Find all paths in the diagram? 1 Point C. Find the critical path? 0.5 Point D. Find the path slack? 0.5 Point E. Calculate the ES, EF, LS and LF times of each activities? 2 Point F. Calculate the activity slack for all activities? 1 Point 7. Belay Ab’ Motors Truck Rental firm has accumulated extra trucks at three of its truck leasing outlets, as shown in the following table: Leasing Outlet Extra Trucks 1. Addis Ababa 70 2. Adama 115 3. Bishoftu 100 Total 285 The firm also has four outlets with shortages of rental trucks, as follows: Leasing Outlet Truck Shortage A. Mekelle 80 B. Semera 50 C. Bahirdar 90 D. Jigjiga 25 Total 245 The firm wants to transfer trucks from those outlets with extras to those with shortages at the minimum total cost. The following costs of transporting these trucks from city to city have been determined: To (cost) From A B C D 1 $7 $8 $4 $9 2 12 4 3 7 3 11 6 7 8 A. Formulate the LP model? 1 Point B. Calculate the initial feasible solution by using NWCM? 1 Point C. Calculate the initial feasible solution by using LCM? 1 Point D. Calculate the initial feasible solution by using VAM? 2 Points 8. Mr. Abebe is establishing an investment portfolio that will include stock and bond funds. he has $720,000 to invest, and he does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund he plans to invest in is 18%, whereas the average annual return for the bond fund is 6%. he further estimates that the most he could lose in the next year in the stock fund is 22%, whereas the most he could lose in the bond fund is 5%. To reduce her risk, he wants to limit her potential maximum losses to $100,000. a. Formulate a linear programming model for this problem. 3 Points b. Solve this model by using graphic method. 5 Points 9. Marshall Business Trading has hired an advertising firm to determine the types and amount of advertising it should invest in for its stores. The three types of advertising available are television and radio commercials and newspaper advertisement. The Business owner desires to know the number of each type of advertisement it should purchase in order to maximize exposure. It is estimated that each advertisement or commercial will reach the following potential audience and cost the following amount: Exposure (People/Ad or Commercial) Cost Television Commercial $20,000 $15,000 Radio Commercial 12,000 6,000 Newspaper Advertisement 9,000 4,000 • The company must consider the following resource constraints: ? The budget limit for advertising is $100,000. ? The television station has time available for 4 commercials. ? The radio station has time available for 10 commercials. ? The newspaper has space available for 7 ads. ? The advertising agency has time and staff available for producing no more than a total of 15 commercials and/or ads. Required: - Please formulate the linear programming model?