Please answer these numerical questions for OPM $625.$

Part III. $6$ numerical problems:

$1.$ 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$

$2.$ 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$

$3.$ 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$.3\mathrm{.}33$

$4.$ The demand data for a firm are given below

Year Quarter Demand

$11110$

$2400$

$3350$

$4200$

$25220$

$6420$

$7380$

$8240$

$39260$

$10470$

$11430$

$12270$

The trend line has been calculated as Y $=250+10$X where Y is demand and X refers to quarters. The forecast for the third quarter of the fourth year will be

A$.400$

B$.456$

C$.484$

D$.496$

E$.520$

$5.$ The following table gives monthly demand for a product.

Month Demand

$16$

$213$

$316$

$423$

Using regression analysis, the forecast for the fifth month is

A$.26\mathrm{.}0$

B$.26\mathrm{.}5$

C$.28\mathrm{.}0$

D$.33\mathrm{.}4$

$6.$ The demand for a product during the last four months is given below

January $850$

February $900$

March $975$

April $950$

The forecast for January was $800.$ Using exponential smoothing with $\backslash$alpha $=0\mathrm{.}3,$ the

forecast for May will be

A$.840\mathrm{.}500$

B$.901\mathrm{.}595$

C$.950\mathrm{.}785$

D$.990\mathrm{.}400$