There is a retailer called \"The Coop\", which carries a widevariety of products with MIT's name and logo: shirts, caps,keychains, pens... you name it! Anything from golf balls and teddybears to pocket protectors and jewelry. With a store inside MIT'sStudent Center, and another one in the popular Kendall Square,across the street from MIT campus, The Coop is a favorite stop forcasual MIT visitors, current students and their relatives, andnostalgic alumni.
The Coop carries a line of products that feature MIT's officialseal cast in a jewelry-grade steel. The same seal (about the sizeof a coin) is used in multiple finished goods, such as necklaces,tie pins, cufflinks, and paperweights. The Coop is consideringintroducing in 2018 a new line of products featuring MIT's sealcast in 18 karat gold. These seals would be used in upscalejewelry, and as an ornament in the diploma frames that sellespecially during commencement season.
Based on their experience with similar products in the past, TheCoop has projected the following demand for gold MIT seals for eachmonth of 2018.
| January | February | March | April |
| 1300 | 300 | 600 | 500 |
| May | June | July | August |
| 2000 | 5500 | 1800 | 1400 |
| September | October | November | December |
| 600 | 500 | 1000 | 2500 |
The seals would be produced, under license, by Seventh Seal, aspecialty manufacturer of commemorative seals cast in preciousmetals, located in Syracuse, New York. Seventh Seal has offered toproduce the gold MIT seals exclusively for The Coop. Seventh Sealhas explained to The Coop that there is a cost to setting up theequipment to produce the gold MIT seal. Because of this, SeventhSeal will charge The Coop a set-up cost of $1417.5 every time theMIT seal is produced.
Because of the high set-up cost, one of the managers at The Coopproposes doing all the seals that will be needed for 2018 in aone-time production batch. \"This will save us a lot of money inset-up costs\", he says.
Another manager, however, warns that - because the gold sealsare expensive - there is an associated holding cost. The Coopestimates that the holding cost will be about $0.21000000000000002per seal per month (the dot is a decimal mark).
Because of the high holding costs, that manager proposes doingmonthly batches in the amount of seals that will be required thatmonth, according to the demand projection. \"This will save us a lotof money in holding costs\", she says.
What are the total costs (e.g. the sum of set-up costs andholding costs) of producing the gold seals using a lot for lot (orchase) approach and a one time approach?
