Q$1.($Total $25$ points$)$

Joanna is currently working a total of $7$ hours per day to produce $280$ dolls. She thinks that by changing the paint used for the facial features and fingernails, she can increase the rate to $360$ dolls per day. Total material cost for each doll is approximately $$3\mathrm{.}50$; she has to spend $$40$ in the necessary supplies $($expendables$)$ per day; energy costs are assumed to be only $$4\mathrm{.}00$ per day; and the labor rate for her is $$10$ per hour.

a$)$ Viewing this from a total $($multifactor$)$ productivity perspective, what is her productivity at present and what is her productivity with the new paint in terms of dolls per dollar? $(15$ points$)$

b$)$ If she uses the new paint, by what amount could Joanna$$s material costs per doll increase without reducing total $($multifactor$)$ productivity? $(10$ points$)$

Q$2.($Total $50$ points$)$

Suppose you $($or your group$)$ are the manager of a company trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecasts for each given forecasting method and then choose the best one to do the forecasts for the future.

Actual

Month Demand

$163$

$265$

$368$

$470$

$572$

$675$

a$.$ Calculate the simple $3-$month moving average forecast for periods $4-6.(5$ points$)$

b$.$ Calculate the weighted $3-$month moving average using weights of $0\mathrm{.}50,0\mathrm{.}30,$ and $0\mathrm{.}20$ for periods $4-6.(5$ points$)$

c$.$ Calculate the exponential smoothing forecast for periods $2-6$ using an initial forecast $($F$1)62,$ and an $$ of $0\mathrm{.}30.(10$ points$)$

d$.$ Calculate the double exponential smoothing forecast for periods $2-6$ using an initial trend forecast $($T$1)$ of $2\mathrm{.}0,$ and initial exponential smoothing forecast $($S$1)$ of $60$ an $$ of $0\mathrm{.}30$ and a $$ of $0\mathrm{.}30.(15$ points$)$

e$.$ Calculate the Mean Absolute Deviation $($MAD$)$ for the forecasts made by each technique in periods $4-6.$ Which forecasting method do you prefer? Using your preferred technique forecast the demands for the following $2$ months $($months $7-8).(15$ points$)$

Q$3.($Total $25$ points$)$

Goodyear Tire and Rubber Company is the ninth largest tire manufacturer in the world. Here are the sales revenues for year $1$ through year $5$:

Year Revenue $($millions$)$

$1$ $$3,889\mathrm{.}9$

$24,066\mathrm{.}4$

$34,535\mathrm{.}6$

$44,731\mathrm{.}8$

$54,498\mathrm{.}7$

a$.$ When might a manager prefer linear trend technique to simple moving average technique? Explain your answer. $(5$ points$)$

b$.$ Based on MAD for from year $3$ to year $5,$ which method $($linear$-$trend or double exponential smoothing method with $=0\mathrm{.}4$ and $=0\mathrm{.}2($start with initial estimates S$1=$ $$4,867\mathrm{.}90$ and T$1=$ $$201\mathrm{.}5$ for the year $1))$ provides the better forecasts? Explain. Forecast the sales revenue for year $6$ and year $7$ based on your preferred method $(20$ points$)$