HW$6/$Separate$,$ Batching, & Matching

Catherine Julson has just taken an engineering class where they designed a product named Woody

Footstool and the associated manufacturing process. The footstools will be produced as an

unfinished furniture kit. Catherine has decided that all the effort should be put to work to support

her education$$so she plans to actually make the footstool kits in her father$$s shop. She has been

assured by her friend, Jaclyn, that there is a market for the footstools and that she can sell all that

Catherine can produce. Catherine does not want to hire any employees or buy any additional

equipment until she sees if this is going to be profitable or not.

Catherine does have data from her class about the steps of manufacture and the time that each step

takes as follows:

$1)$ Receive leg stock each morning between $7$:$00$ am and $8$:$00$ am and cut into legs. Legs arrive in

batches of six. Each piece of leg stock can be cut into four legs and takes a uniformly distributed $3$

to $7$ minutes to cut all four legs from each piece of leg stock. Some light sanding is done as a part

of this process but is included in the above process time. This process requires her father$$s only

chop saw and, of course, Catherine will run it$.$ Since some of the wood has knots, $5\%$ of the legs

will be discarded as waste.

$2)$ Receive seat stock each morning between $7$:$00$ am and $8$:$00$ am and cut into seats. Seats arrive

in batches of two. Each piece of seat stock yields five seats and takes $15$ to $25$ minutes of time per

piece of seat stock, uniformly distributed. Some light sanding is done as a part of this process but

is included in the above process time. Again, this requires Catherine and the same chop saw. Loss

is considered to be negligible in this process.

$3)$ Receive hardware each morning between $7$:$00$ am and $8$:$00$ am in batches of $5.$ No additional

work is needed.

$4)$ Catherine$$s father wants her to keep the WIP $($Work in Process$)$ inventory as low as possible so

he can walk through the shop without tripping over anything. So don$$t order too much.

$5)$ Collect all the wood pieces and the hardware $($one seat, one pack of hardware, and a set of four

legs$).$ Package the stool pieces into a kit for shipment. This requires a normally distributed mean

of $8$ minutes with a standard deviation of $0\mathrm{.}5$ minutes. Again, the work is performed by Catherine.

Catherine has the following questions that she needs for you to answer. Catherine wants only to

work a standard eight hour day $($between $8$:$00$am and $5$:$00$pm with lunch between $12$:$00-1$:$00$

because she is going to night school$).$ You can assume that Catherine ends the day after eight hours

and resumes the next day where she stopped the previous day:

$$ Catherine wants you to help her maximize her output to make the most money. So what is

the most stools $($on average$)$ that she can make on a daily basis? $($total number out divided

by $15$ days$)$

$$ At maximum output, she wants to know how much she runs the chop saw on a daily

average. What would the chop saw$$s average utilization be$?($see output report$)$