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.

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