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$1)(16$ 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 $?$