Question

Abrasives Corp. manufactures industrial diamonds for use in the cutting, machining and drilling industries. They produce the highest quality diamonds in the industry, and can sell any amount they can produce for $5 per carat. Abrasive Corp runs 24 hours per day, 7 days per week. Abrasive Corp.’s production process has six steps:

• Graphite Core Manufacturing: There are two machines, each capable of producing 14 cores per hour.
• Ceramic Tube Manufacturing: There are three machines, each capable of producing 16 tubes per hour.
• Ceramic End Cap Manufacturing: There are four machines, each capable of producing 20 end caps per hour.
• Cell Assembly. A complete cell is produced by placing the graphite core in the ceramic tube and closing each end of the ceramic tube using an end cap, i.e., two end caps in total per cell. One person can assemble a cell in 3 minutes. There are 2 people working in cell assembly.
• Pressing. Each cell is placed in a single machine, where it is subjected to high pressures and temperatures. Each cell produces 50 carats of diamond. A machine can process one cell per hour. There are 22 pressing machines.
• Separation. The diamonds produced during pressing need to be separated from the graphite. This requires a special chemical treatment in a reactor. A reactor (a type of machine) processes the cells in batches of 100. It takes 35 seconds per cell to load the reactor. Regardless of how many cells are processed, the reactor must be run for 8 hours after being loaded. At that point, the reactor is unloaded. It takes 20 seconds per cell to unload the reactor. There are two reactors.

What is the capacity of Core Manufacturing (in carats per hour)?

What is the capacity of Ceramic Tube Manufacturing (in carats per hour)?

What is the capacity of Cell assembly (in carats per hour)?

What is the capacity of Pressing (in carats per hour)?

What is the capacity of Separation (in carats per hour)?

Answer 1

Answer:

Formula for capacity is given as:

Capacity = operating hours x operating rate x the number of machine

Capacity of Core Manufacturing (in carats per hour) = 1 x 14 x 2 = 28 carats per hour

Capacity of Ceramic Tube Manufacturing (in carats per hour) = 1 x 16 x 3 = 48 carats per hour

Capacity of Cell assembly (in carats per hour) = 1 x 4 x 20 x 2 x 3 x 2 = 960 carats per hour

Capacity of cell assembly includes the capacity of Ceramic End Cap Manufacturing and hence, it is taken as (4 x 20) and cell assemble has two end caps taking 3 minutes by 2 person, therefore, their capacity is taken as (2 x 3 x 2)

Capacity of Pressing (in carats per hour) = 1 x 50 x 22 = 1100 carats per hour

Capacity of Separation (in carats per hour) = 3600 x 100 x 2 / 55 = 13091 carats per second = 13091/3600 = 3.63 carats per hour