Question #1. (2 Marks) Consider the network shown below. a. Develop a mathematical model that determine the shortest route between the origin and the destination. b. Solve it using software and show the results. c. What is the shortest route between 1 and 7? d. Which route corresponding with the optimal solution in part b above should be followed? 2 31 5 85 61 72 7 53 3 117 24 88 65 137 6 Answer: a. Question #2. (3 Marks) Consider the table below showing the activities that comprise a project. Each activity's estimated completion time (in weeks) and immediate predecessors are listed as well. Draw the project diagram. b. Determine the expected total time to complete the project. c. Determine the slack for each activity. d. Determine all critical paths and critical activities. e. How many weeks correspond with 80% project completion? f. What is the probability that the project can be completed in 40 weeks? Predecessors a Activity 1 1 2 2 E 009191 ANOS 3 3 4 1 4 4 5 1 5 6 3 3 6 2 6 blog 7 7 3 3, 5, 6 3, 5, 6 DINI 8 8 9 15 12 20 9 10 5 10 4 7 5 11 11 6 7,9 8, 11 12 12 8 3 ANSWER: Question # 3. (3 Marks) Hadiid Steel Co. trying to determine how to minimize the annual costs associated with purchasing steel scrap for its raw material. Each time an order is placed an ordering cost of $150 is incurred. The price of steel scrap depends on q, the weight of steel scrap ordered (in tons). The annual holding cost is 20% of the dollar value of inventory. During each month, the company uses 50 tons of steel scrap. Determine: a. the optimal order quantity and b. the number of orders placed each year. No. of steel scrap Ordered (tons) Price per ton q