GA: Gold MIT Seals

There is a retailer called "The Coop", which carries a wide variety of products with MIT's name and logo: shirts, caps, keychains, pens... you name it! Anything from golf balls and teddy bears to pocket protectors and jewelry. With a store inside MIT's Student Center, and another one in the popular Kendall Square, across the street from MIT campus, The Coop is a favorite stop for casual MIT visitors, current students and their relatives, and nostalgic alumni.

The Coop carries a line of products that feature MIT's official seal cast in a jewelry-grade steel. The same seal (about the size of a coin) is used in multiple finished goods, such as necklaces, tie pins, cufflinks, and paperweights. The Coop is considering introducing in 2018 a new line of products featuring MIT's seal cast in 18 karat gold. These seals would be used in upscale jewelry, and as an ornament in the diploma frames that sell especially during commencement season.

Part 1

Based on their experience with similar products in the past, The Coop has projected the following demand for gold MIT seals for each month of 2018.

January	February	March	April
130	30	60	50

May	June	July	August
200	550	180	140

September	October	November	December
60	50	100	250

The seals would be produced, under license, by Seventh Seal, a specialty manufacturer of commemorative seals cast in precious metals, located in Syracuse, New York. Seventh Seal has offered to produce the gold MIT seals exclusively for The Coop. Seventh Seal has explained to The Coop that there is a cost to setting up the equipment to produce the gold MIT seal. Because of this, Seventh Seal will charge The Coop a set-up cost of $1134 every time the MIT seal is produced.

Because of the high set-up cost, one of the managers at The Coop proposes doing all the seals that will be needed for 2018 in a one-time production batch. "This will save us a lot of money in set-up costs", he says.

Another manager, however, warns that - because the gold seals are expensive - there is an associated holding cost. The Coop estimates that the holding cost will be about $1.68 per seal per month.

Because of the high holding costs, that manager proposes doing monthly batches in the amount of seals that will be required that month, according to the demand projection. "This will save us a lot of money in holding costs", she says.

They ask for your help in evaluating some alternatives.

What is the total cost (e.g. the sum of set-up costs and holding costs) of producing the gold seals using a lot for lot (or chase) approach?

In this and every other question in this problem that asks for a cost, enter your answer in dollars, without currency symbol or thousands commas. For example, if the cost is $1,234.56 then type 1234.56 as your answer.

Part 2

What is the total cost (e.g. the sum of set-up costs and holding costs) of producing the gold seals using a one time run approach?

Part 3

What is the total cost (e.g. the sum of set-up costs and holding costs) of producing the gold seals using a Silver-Meal algorithm?

Part 4

What is the total cost (e.g. the sum of set-up costs and holding costs) of producing the gold seals using an optimal solution?