Assignment $2-$ Learning Curve

Part $1$:

The first unit took $24$ hours of labor to produce. The company has experienced a $90\%$ learning curve when producing similar designs. The company is interested in estimating the total time and cost to complete the next $15$ units. So$,$ your job as the production cost estimator is to prepare the estimate. Knowing that $200$ hours are available, $$1,100$ is the available budget for the labor cost and company pays $$4\mathrm{.}5$ per hour for its labor:

Develop a learning curve model to show how time and direct labor costs decrease with learning.

Does the company have adequate time to produce all the $15$ units?

Estimate the time and the labor cost it will take to complete the $4^{th}$ unit.

How much would the company expect to pay as labor costs for all the $15$ units?

If the company affords only $$1,100$ as labor cost? How many units can be produced within the available budget for the labor cost?

What would be the new learning rate, if the company could pay only $$1,100$ for all the $15$ units?

With the new learning rate, how many units can be produced within the $200$ available hours? And what would be the total cost of these units? How much will be the remaining budget?

Part $2$:

Even with the new learning rate $($Q$6)$ the company is not able to finish the $15$ units within the available time $(200$ hours$).$ Therefore, the company is considering the introduction of a subcontractor to produce the remaining units within the remaining budget. The company wants to know whether to select Subcontractor #$1$ or #$2$ to continue.

$\backslash$table$[[$Subcontractor #$1,$Subcontractor #$2],[$Units$,$Time in hours,Units,Time in hours,$],[2,19\mathrm{.}85,8,13\mathrm{.}02,],[4,15\mathrm{.}88,16,10\mathrm{.}67,]]$

The company is concerned in estimating the total time and cost for each subcontractor to complete the remaining units:

Develop a learning curve model for each subcontractor for $10$ units.

If company expects to buy $8^{th}$ and $9^{th}$ units from Subcontractor #$1$:

a$.$ How long it took to produce them?

b$.$ What would be your expected cost for the company if Subcontractor #$1$ charges $$4\mathrm{.}75$ for each labor$-$hour?

If company expects to buy $9^{th}$ and ${10}^{th}$ company from Subcontractor #$2$ :

a$.$ How long it took to produce them?

b$.$ What would be your expected cost for the company if Subcontractor #$2$ charges $$4\mathrm{.}5$ for each labor$-$hour?

Should you encourage Subcontractor $A$ or $B$ to continue? Why?