Answer :
If a machine operator can program machine #1 to produce 100 parts per hour, but the machine requires 2 hours of service each day when it is not operating and machine #2 can produce only 80 parts per hour, but only requires 30 minutes of service each day, then both the machines are equal in productivity in an eight hour work day.
To determine which machine is more productive in an eight hour work day, an algebraic expression can be used.
x = y ( 8 hours - s )
Here, x = to the parts produced in an eight hour work day
y = parts produced per hour
s = service hours
Thus, the parts produced by both the machines in an eight hours work day can be calculated using this algebraic expression as follows,
For Machine #1:
y = 100 and s = 2
x = 100 ( 6 )
x = 600
Machine #2:
y = 80 and s = 0.5
x = 80 ( 8 - 0.5 )
x = 80 ( 7.5 )
x = 600
Hence, both machines are equally productive in an eight hour work day.
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Both Machine #1 and Machine #2 can produce 600 parts in an eight-hour workday. In this scenario, neither machine is inherently more productive in terms of total parts produced.
Step 1: Analyze Machine Capabilities
Machine #1:
- Produces 100 parts per hour.
- Requires 2 hours of service daily (which means it's not producing during this time).
Machine #2:
- Produces 80 parts per hour.
- Requires only 30 minutes (0.5 hours) of service daily.
Step 2: Calculate Available Production Time
An eight-hour workday translates to 8 hours of potential production time. However, we need to factor in the service time for each machine.
Machine #1 available time:
- Total workday hours - Service time = 8 hours - 2 hours = 6 hours
- Machine #2 available time:
- Total workday hours - Service time = 8 hours - 0.5 hours = 7.5 hours
Step 3: Compare Production Output
Now that we know the available production time for each machine, we can calculate their total output in an eight-hour workday.
- Machine #1 production:
- Production rate * Available time = 100 parts/hour * 6 hours = 600 parts
- Machine #2 production:
- Production rate * Available time = 80 parts/hour * 7.5 hours = 600 parts
