A small metal casting company has the opportunity to produce a custom gear part for a high performance application using AM. They currently have an offer from a service provider to print sand molds and cores at a cost of $100/mold, with a material cost of $10/kg of sand. Traditional sand casting for this gear part requires a mold that costs $50 and uses 5 kilograms of sand per mold, with a material cost of $2/kg of sand. The gear part has a volume of 300 cm³, and the density of the sand used for casting is 1.6 g/cm³. The AM process can reduce lead time from 2 weeks to 3 days. The company needs to decide if they should accept the offer from the service provider to use AM for this part. They plan to produce a batch of 50 gears. 

a) Calculate the total cost of producing the sand molds using traditional casting and compare it to the AM cost. 

b) Determine the total material cost for the sand needed for 50 gears in traditional casting and AM. 

c) Assess the total savings in time if the company decides to go with AM instead of traditional casting.