(Solved): Atlas Inc. is a toy bicycle manufacturing company producing a five-inch small

Atlas Inc. is a toy bicycle manufacturing company producing a five-inch small version of the bike that Lance Armstrong rode to win his first Tour de France. The assemblyline at Atlas Inc. consists of seven work stations, each performing a single step. Stations and processing times are summarized here:
• Step 1 (35 sec.): The plastic tube for the frame is cut to size.
• Step 2 (25 sec.): The tube is put together.
• Step 3 (35 sec.): The frame is glued together
• Step 4 (30 sec.): The frame is cleaned.
• Step 5 (25 sec.): Paint is sprayed onto the frame.
• Step 6 (45 sec.): Wheels are assembled.
• Step 7 (35 sec.): All other parts are assembled to the frame.
Under the current process layout, workers are allocated to the stations as shown here:
• Worker 1: Steps 1, 2
• Worker 2: Steps 3, 4
• Worker 3: Step 5
• Worker 4: Step 6
• Worker 5: Step 7
Assume the workers are paid $15 per hour. Each bicycle is sold for $5 and includes parts that are sourced for $1. The company has fixed costs of $225 per hour. Despite Lance Armstrong’s doping confession, there exists substantially more demand for the bicycle than Atlas can supply.
Instructions: Round all answers to 2 decimal places. Negative amounts should be indicated by a minus sign.
a. What is the cost of direct labor for the bicycle? $0.23 per unit
b. How much profit does the company make per hour? per hour
c. What would be the profits per hour if Atlas would be able to source the parts 11% cheaper ($0.89 for the parts of one unit, but the fixed costs and productivity will remain same as before)? per hour
d. What would be the profits per hour if Atlas would be able to reduce fixed costs by 12% (to $198.00 per hour)? per hour
e. What would be the profits per hour if Atlas would be able to reduce the processing time at the bottleneck by 3 seconds per unit (assume unlimited demand, note that reducing the processing time may cause the bottleneck to shift to a different process or create multiple, identical bottlenecks)? per hour

Expert Answer


a. Maximum time is used by worker 2 to cover step 3 and 4. He consumes 30+35= 65 seconds. This is the limiting factor/bottleneck for the line.

In one hour (at one assembly line):

No. of cycles produced= 1hour/ 65 seconds= 3600 seconds/65 seconds = 55.38 cycles

Cost encurred = cost per worker per hour* number of workers= 15*5= $ 75

Hence, direct labor cost per bicycle= 75/55.38= $ 1.35

b. Fixed cost for one assembly line per hour is $ 75. It is given that total fixed cost per hour is $ 225. Hence, there are 3 assembly lines.

Profit= Price- cost

Price (per hour)= number of cycles per hour on one line*number of lines* sale price of each bicycle= 55.38*3*5= 830.7

Cost (per hour)= Fixed cost+variable cost= 225+ (55.38*3*1)= 391.14

Hence, Profit per hour= 830.7 – 391.14= $ 439.56

c. The price and fixed cost would not be affected, only variable cost would be affected.

Profit per hour= 830.7 – (225 +(55.38*3*0.89)) = $ 457.83

d. If only fixed cost is affected and price and variable costs are not affected then

Profit per hour= 830.7 – ( 198+ (55.38*3*1))= $ 466.56

e. If bottleneck time is reduced by 3 seconds i.e. to 62 seconds from 65 seconds:

No. of cycles produced per assembly line per hour= 1hour/ 62 seconds= 3600 seconds/62 seconds = 58.06 cycles

cycle produced per hour= 58.06*3= 174.19

Profit per hour= (174.19 * 5) – (225+(174.19*1))= 870.95 – 399.19 = $ 471.76

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