Problem 1: Resource allocation Given the following activities for staging a community play on Independence Day, a) Calculated the expected time and variance of each activity. b) Draw an AON diagram with ES, EF, LS, LF. c) What is the project duration and standard deviation? d) What is the probability to finish the project in 45 days? 42 days? 38days? e) How many days will be needed to finish the project with 80% probability? 95% probability? Activity Predecessor Time (days) a m b A 2 4 6 B 5 5 5 C B 3 5 7 D A 7 9 11 E A 11 12 13 TI B, D 5 6 7 G C 9 10 11 H C, F 10 D 9 11 J E 3 3 3 K F 8 10 12 L H 8 10 M I, J 7 15 N G 10 12 14 O L, M 4 6 8Problem 2: Resource allocation Please use the following information to develop a project plan. In addition to the project activity cost there is a overhead cost of $20/day. The client wants the project to finish by 6 days and they imposed a penalty of $50 per day after day 6, also they will pay a bonus of $50 per day if the project finishes before day 6. What is your suggestion for the company? Please show all your network diagrams and calculations for each day with a graph showing total cost against number of days. Activity Precedence Duration, Days (normal, crash) Cost (normal, crash) 3, 2 $ 40. 80 2, 1 20, 80 2, 2 20, 20 4, 1 30, 120 * * 3, 1 10, 80 *Partial crashing allowed * Partial crashing not allowedProblem 3: Decision Analysis Charles is considering three investment options for a small inheritance that he has just received - stocks, bonds, and money markets. The return of his investment depends on the performance of the economy, which can be strong, average, or weak. The returns for each possible combination are shown in the following table: PAYOFFS Outcomes Alternatives Strong Average Weak Stocks 15% 5% -10% Bonds 8% 5% -1% Money Market 5% 3% 1% Probability 0.2 0.35 0.45 a. Which investment should Charles choose if he uses Maximax criterion? b. Which investment should Charles choose if he uses maximin criterion? c. Which investment should Charles choose if he uses equally likely criterion? d. Which investment should Charles choose if he uses the criterion of realism with alpha = 0.5? e. Which investment should Charles choose if he uses minimax regret criterion? f. Using EMVs, which option should Charles choose? What is the maximum EMV? g. Using EOL, which option should Charles choose? What is the minimum EOL? h. Compute the EVPI and show that it is the same as the minimum EOL.WW ABC Beverage Company has soft drink product that has a constant demand rate of 36,000 cases. A case of soft drink costs ABC $4. Ordering costs are $20 per order and holding costs are 20% of the value of inventory. ABC has 250 days per year and the lead time is 5 days. Identify the following aspects of the inventory policy for ABC. a. Currently ABC is using an order size of6,000 cases. As a management consultant how can you help them? b. What would be the new Reorder point? Cycle time? Total annual cost? mumml XYZ Company produce books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7,20000pies. The cost of one copy of the book is $14.50. The holding cost is based on an 18% annual rate, and setup costs are $150 per setup. The equipment on which the book is produced has an annual production volume of 27,000 copies. XYZ has 300 working days per year, and the lead time for a production run is 15 days. Answers the following aspects of the inventory policy for XYZ. a. Currently the company is using EOQ model for determining their order size. As a management consultant how can you help them to reduce inventory cost? b. What would be the i. Minimum cost production lot size? ii. Number of production runs per year? iii. Cycle time? iv. Length of a production run. v. Max. inventory? vi. Reorder point? vii. Total annual cost