Question $1(16$ marks$)$: Your boss is the project manager for a large contract assembly plant. A new customer has come to you with a product they want $20$ units of assembled. The customer

estimates that the time to assemble a unit is about $16$ hours to assemble each one and is willing to pay you at that rate. She offers you the project. You want to impress the boss, but you don't want to take the project if it will lose money and make you look bad. She

tells you that the first unit took $30$ hours, and the second one took $24$ hours.

a$)$ What is the learning rate for this project? How many hours do you expect the third unit to take? How many hours do you expect the $20^("$th $")$ unit to take? What is the percentage change in productivity from the first unit to the $20^("$th $")$ unit?

b$)$ What is the total number of hours required for all $20$ units? What is the average time to assemble all of the units? Should you accept the project? Why or why not?

c$)$ After you have finished the project, the company comes back and asks for $20$ more units. How long do believe the first unit of the order would take to produce? The $20^("$th $")?$ How many labour hours would be required for the second order? What is the labour time per

unit?

d$)$ Suppose your company can supply $603\mathrm{.}66$ labour hours per month to this product. What is your "capacity" to produce this product $($i$.$e$.$ how many can you produce in the first month$)?$

e$)$ You have another product with a learning curve of $0\mathrm{.}73$ and the first unit took $20$ hours. How long with the $3^("$rd $")$ unit take? The $7^("$th $")?$

Question $2(18$ marks$)$: You have been contracted to undertake a project for a firm. The project parameters are listed in the table below.

a$)$ Draw a network diagram and determine the critical path for the project. What is the expected completion time $($state it explicitly$)?$

b$)$ The client asks you to shorten the project by $3$ weeks and will pay you a bonus of $$1,200.$ Is this worthwhile?

Question $3(18$ marks$)$: An advertising agency CEO has gathered the activity information for a new advertising campaign as shown in the accompanying table.

Activity Time estimate weeks Optimistic Most Likely Pessimistic

Immediate Predecessors

A $147-$ B $267-$ C $336$ B D $61314$ A E $3612$ A$,$C F $6816$ B G $156$ E$,$F

a$)$ Draw the network diagram. What is the expect completion time $($state it explicitly$)?$ What is the variance of project completion time?

b$)$ The deadline is $23$ weeks. What is the probability of completing it on time? What is the probability of the project missing the deadline?

c$)$ As project manager, you will be paid a bonus if you finish the project in $19$ weeks. What is the probability of achieving the bonus?

d$)$ What is the probability of finishing between $19$ and $23$ weeks?

e$)$ What is the timeline that would achieve a $60\%$ probability of finishing?