Problem 3: (20 points) A start-up has developed a new autonomous meal kit delivery cart. The following activities must take place to assemble a prototype and test it. 1 1. Draw the network diagram for this project. ( 1pt) 2. Find the critical path and determine the expected completion date. What is the total project cost? ( 4 pts) 3. Based on the critical path found above, use the standard normal distribution to find the probability that the project will take between 18 and 20 weeks to complete. (2 pts) 4. Find the number of weeks required to complete the project with probability 99%. (3 pts) The duration of the following activities can be reduced by up to 2 weeks at the indicated cost. per week: (A,$30,000);(B,$30,000);(C,$70,000); (D, \$25,000). The other activities cannot be crashed. 5. Based on the expected durations, which activity(ies) should be crashed to reduce the project length by 4 weeks at a minimum cost? What will be the total project cost? Provide all details, You can use Excel or GLPK/Gusek or Python. (10 pts)