<p>Final Exam DS 523 Spring 2008</p><p>1.A project network is shown below. Use a forward and a backward pass to determine the critical path, and then fill out the table below.</p><p>Precedence Activity Critical Activity Activities Time (weeks) ES LS EF LF Slack Path? A B C D E F G H I</p><p>Now assume that the times listed are only the expected times instead of being fixed times. Is the probability of being finished in fewer than 25 weeks more or less than 50%? 2.Given the following network with activities and times estimated in days,</p><p>Most Activity Optimistic Probable Pessimistic A 2 5 6 B 1 3 7 C 6 7 10 D 5 12 14 E 3 4 5 F 8 9 12 G 4 6 8 H 3 6 8 I 5 7 12 J 12 13 14 K 1 3 4</p><p> a. What are the critical path activities? b. What is the expected time to complete the project? c. What is the probability the project will take more than 28 days to complete? 3. A payoff table is given as</p><p>State of Nature</p><p>Decision s1 s2 s3</p><p> d1 250 750 500 d2 300 250 1200 d3 500 500 600 a. What choice should be made by the optimistic decision maker? b. What choice should be made by the conservative decision maker? c. What decision should be made under minimax regret? d. If the probabilities of s1, s2, and s3 are .2, .5, and .3, respectively, then what choice should be made under expected value? e. What is the EVPI? 4. Fold back this decision tree. Clearly state the decision strategy you determine. 5. The Tiernan Gallery and Art Museum distributes to its visitors a printed guide to its collections. There are about 18000 visitors per year. Holding costs for the brochures are 20% and it costs $30 to place an order with the printer. The printer has offered the following discount schedule:</p><p>Category Order Size Unit Cost 1 0 - 1499 $2.50 2 1500 - 2999 $2.20 3 3000 and over $1.80</p><p>How many brochures should be printed at a time?</p><p>6.The Fitness Shop is considering ordering a special model exercise machine. Each unit will cost the shop $410 and it will sell for $750. Any units not sold at the regular price will be sold at the year-end model clearance for $340. Assume that demand follows a normal probability distribution with  = 20 and  = 6. What is the recommended order quantity?</p>