Borges Machine$$ Shop, Inc., has a$1-$year contract for the production of

$225$ comma $000225,000$

gear housings for a new$$ off$-$road vehicle. Owner Luis Borges hopes the contract will be extended and the volume increased next year. Borges has developed costs for three alternatives. They are$$ general$-$purpose equipment$($GPE$),$ flexible manufacturing system$($FMS$),$ and$$ expensive, but$$ efficient, dedicated machine$($DM$).$ The cost data$$ follow:

$$

$$General$-$Purpose Equipment$($GPE$)$

Flexible Manufacturing System$($FMS$)$

Dedicated Machine$($DM$)$

Annual contracted units

$225$ comma $000225,000$

$225$ comma $000225,000$

$225$ comma $000225,000$

Annual fixed cost

$ $125$ comma $000$$$125,000$

$ $225$ comma $000$$$225,000$

$ $500$ comma $000$$$500,000$

Per unit variable cost

$ $16\mathrm{.}00$$$16\mathrm{.}00$

$ $14\mathrm{.}75$$$14\mathrm{.}75$

$ $13\mathrm{.}50$$$13\mathrm{.}50$

Part $2$

Based on the$$ cost$,$ the process that is best suited for the current contracted volume is

GPE

$.$

$$

Week

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Demand

$1919$

$2020$

$2929$

$3636$

$2424$

$2828$

$3636$

$2424$

$2626$

$2929$

Part $2$

$$a$)$ The forecast for weeks $2$ through $10$ using exponential smoothing with

alpha

$=$

$0\mathrm{.}550\mathrm{.}55$

and a week $1$ initial forecast of

$19\mathrm{.}019\mathrm{.}0$

are $($round your responses to two decimal$$ places$)$:

Week

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Demand

$1919$

$2020$

$2929$

$3636$

$2424$

$2828$

$3636$

$2424$

$2626$

$2929$

Forecast

$19\mathrm{.}019\mathrm{.}0$

$19\mathrm{.}019\mathrm{.}0$

$19\mathrm{.}5519\mathrm{.}55$

$24\mathrm{.}7524\mathrm{.}75$

$30\mathrm{.}9430\mathrm{.}94$

$27\mathrm{.}1227\mathrm{.}12$

$27\mathrm{.}6027\mathrm{.}60$

$32\mathrm{.}2232\mathrm{.}22$

$27\mathrm{.}7027\mathrm{.}70$

$26\mathrm{.}7726\mathrm{.}77$

Part $3$

$$b$)$ For the forecast developed using exponential smoothing

$($alpha

$=$

$0\mathrm{.}550\mathrm{.}55$

and initial forecast

$19\mathrm{.}019\mathrm{.}0),$

the MAD$=$

$5\mathrm{.}015\mathrm{.}01$

sales $($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ For the forecast developed using exponential smoothing

$($alpha

$=$

$0\mathrm{.}550\mathrm{.}55$

and initial forecast

$19\mathrm{.}019\mathrm{.}0),$

the tracking signal$=$

enter your response here

$($round your response to two decimal$$ place