1: Determine if the following problems are bounded or unbounded and then determine if they are feasible or infeasible (5pts each):

Suppose you have 12 technicians in your organization, each of whom works a 40-hour week with100 % of their time scheduled. Assuming emergency breakdown consumed 89 man-hours out ofthe work schedule. Calculate: a) Total weekly man-hours scheduled b) Scheduled man-hours completed c) Percentage of scheduled compliance

Given the directed graph shown in figure 2 below, determine the following: a) Adjacent matrix b) Incidence matrix c) Edge list d) Adjacent list.

5. Which is the most expensive exclusive site resumption strategies? a. Mobile site b. Cold site С.Warm site d. Hot site e. Mirrored site

Find the shortest path from node 1 to 5 in the figure 3 using Dijkstra Algorithm.

Case 1:(40 Points) A national quality consultation firm has identified the following set of activities thatmust occur to carry out an audit for one of their major clients. As the project manager of thisaudit, answer the following questions related to the project plan. Q1. Draw the Network Diagram of the project plan for the consultation firm. (13 Points) Q2. Answer the following MCQ (Multiple Choice Questions), and justify your answer for the selected questions where the justification box shown (15 Points/ 3 Points Each): 1) What is the expected project completion time:а. 54 days b. 34 days c. 61 days d. 59 days 2)What is the Slack period for task C:a. 12 days b. 3 days c. 4 days d. 11 days 3)What is the task with the longest slack time:а. Task H b. Task F с. Task B d. Task J 4) What is the slack period for task G:a. 6 days b. 5 days c. 8 days d. O days 5) What is the early start for task C:a. Day 12b. Day 25c. Day 19d. Day 16 Q3. Fill in the blank the correct answer for the following statements (12 Points/ 3 Points Each): 1. The critical path the plan is showing in the project 2. The early finish for task H 3. The late start for task D 4. The late finish for task J

Questions: a) Based on your solution, what was the average travel time (in days) for the 100 containers? b) Based on your solution, what was the average percent damage for the 100 containers? c) Which countries did not ship out all their available containers? Why did these countries, as opposed to those who shipped out all their containers, not ship out more containers? Explain.

3. A firm has three types of wood products (X₁, X2, X3) each requires (or potentially requires) four inputs: A B, C and D. The profit contribution of each output is $20, $27 and $34.5, respectively. a. The company's objective is to choose the product mix that maximizes its profit. Write out the objective function and the constraints. b. Find the profit-maximizing solution using EXCEL's Solver. Hand in copies of the answer report and the sensitivity report. c. If you were to give it a two-dimensional interpretation (that is, think of a two product model on a graph), how would you interpret the "allowable increase" for the X3 coefficient? d. Would it be worth for the firm to acquire one more unit of input A if it cost $10 to do so? Explain with reference to the shadow price.

. In solving real world problems, when it is more appropriate to use mathematical modeling instead of qualitative methods? And why the Operations Research modeling approach could be more effective?

3.5-3. Ed Butler is the production manager for the Bilco Corpora- tion, which produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with the following processing times (in hours):