Please provide full workings for each question:

Question 1: (2 marks) You want to purchase a crane for your project and sell it by the end of the project. There are two options available in the market. The buying prices, anticipated incomes, and selling prices for each option are articulated in the table below. Your expected rate of return is 11% and the annual inflation rate is 5%. Using this information, find out which option is the better choice according to payback period and Net Present Value methods? Buying prices Crane 1 Crane 2 $380,000 $420,000 Annual earning Crane 1 Crane 2 2024 $90.000 $110,000 2025 $85.000 $120,000 2026 $90,000 $115,000 2027 $95,000 $112,000 2028 $95,000 $110,000 2029 (selling prices) $250,000 $280,000Question 2: (1 mark) Draw a bar chart for the following project and find the completion time. Pay attention to the activity relationships. Activities Duration Predecessors Activity (Weeks) relationship Start 0 A 5 Start B 10 A FS C 8 B SS D 5 FS E 10 D FF F 5 B, C FS G 10 F SS H 5 F. G FS Finish 0 HlQuestion 3: [2 marks] From the following information. draw the CPM network. Calculate early and late activity times. and slacks [total and free oats). Find the project completion time and highligwt the critical path. Activity ID Duration Predecessors Relationship Lag A 3 B 12 A C 5 A D 2 B C E E B FF 4 C F 10 E 33 2 E FF 3 G 4 D G H E E F Question 4: (2.5 marks) You are appointed as the project manager of a construction firm which has recently signed a redevelopment contract with a horse racing club to make substantial improvements to one of their flagship racecourses. Based on the following project information and CPM network: 1. Calculate the probability of completing the project by the end of week 19. II. Calculate the project duration with 97% confidence level. I. Calculate probability of completing the project before 21. Activity ID Duration (Week] Optimistic Most likely Pessimistic A 2 5 8 B 2 9 C 2 3 10 D 1 2 3 m 4 13 TI 3 5 13 G 1 4 7 B Lag +5 E A D G C FQuestion 5: (2.5 marks) From the following information, answer the questions. Please ensure that you read the blow questions carefully and pay attention to keywords. IV. The probability that the project will finish by the end of day 18 V. The probability that the project will finish by the end of day 24 VI. The probability that the project will finish on the 22nd day VII. The completion date with at least a 99% confidence level Activity Duration (days) Optimistic Most likely Pessimistic A 1 3 7 B 3 5 12 2 2 2 D 5 6 11 E 6 13 F 2 3 5 G 4 4 14 B D A C E G F