Part III. $6$ numerical problems: $7\mathrm{.}5$ Points each. Please mark the answer either by changing the font of the answer to boldface or by writing the answer in the space provided at end of the question. Please do not use colors to mark the answers.

$1.$ A company can produce a small lot of products the first time at a cost of $$10,000.$ If their $75$ percent learning curve allows them to reduce their costs on each lot, what is the total cost of producing $10$ lots? You can look at the tables in the book.

A$.$ $$100,000$

B$.$ $$93,978$

C$.$ $$65,432$

D$.$ $$55,890$

E$.$ $$49,310$

Answer$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$2.$ You are a consultant called in to estimate the costs after the employees learn how to do a job more efficiently by repetition. You find a company can produce a product the first time at a cost of $$2,500.$ If their $65$ percent Learning Curve allows them to reduce their costs on each product, what is the total cost of producing $400$ units of the new product? You can look at the tables in the book.

A$.$ $$100,000$

B$.$ $$78,900$

C$.$ $$58,600$

D$.$ $$45,765$

E$.$ $$37,850$

Answer$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$3.$ If the forecasts for three periods were $20,30,$ and $40$ while actual demands for respective periods were $25,35,$ and $20$ then the tracking signal is

A$.1$

B$.10$

C$.1$

D$.10$

E$.3\mathrm{.}33$

Answer$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$