You are the project manager at a major contract assembly facility. A new client approaches you with an order to assemble

$2$

$5$

$$units of their product. They estimate that the time to assemble one unit is roughly

$1$

$5$

$$hours and agree to compensate you based on that. You want to impress your superior, but you are cautious about taking on a project that could result in losses or reflect poorly on your performance. The client informs you that the first unit took

$2$

$8$

$$hours$,$ and the second one took

$2$

$1$

$$hours$.$

a

$)$

$$What is the learning rate for this task? How many hours do you estimate the third unit will take? What is your expected time for assembling the

$2$

$5$

th unit? What is the percentage improvement in productivity from the first to the

$2$

$5$

th unit?

b

$)$

$$How many total hours will be required to assemble all

$2$

$5$

$$units$?$ What is the average time per unit for the entire batch? Based on these calculations, should you accept the project? Explain your reasoning.