A processor makes two components, A and B, which are packaged together as the final product (each product contains one A and one B).
The processor can do only one component at a time: either it can make As or it can make Bs. There is a setup time when switching from A to B.
Current plans are to make 100 units of component A, then 100 units of component B, then 100 units of component A, then 100 units of component B
and so forth, where the setup time and run time for each component are given below:
Component Setup/Changeover time Run time/unit
A 5 minutes 0.2 minute
B 10 minutes 0.1 minute
Assume the packaging of the two components is totally automated and takes only two seconds per unit of the final product. This packaging time is small enough
that you can ignore it.
What is the average hourly output, in terms of the number of units packaged product (which includes one component A and one component B)?
To calculate the average hourly output, we need to determine the total time it takes to produce one cycle of 100 units of component A and 100 units of component B.
For component A:
Setup time = 5 minutes
Run time per unit = 0.2 minutes
Number of units = 100
Total time for component A = Setup time + (Run time per unit * Number of units) = 5 + (0.2 * 100) = 5 + 20 = 25 minutes
For component B:
Setup time = 10 minutes
Run time per unit = 0.1 minutes
Number of units = 100
Total time for component B = Setup time + (Run time per unit * Number of units) = 10 + (0.1 * 100) = 10 + 10 = 20 minutes
Total time for one cycle (A + B) = Total time for component A + Total time for component B = 25 + 20 = 45 minutes
Now, to calculate the average hourly output, we need to convert the time to hours. There are 60 minutes in an hour.
Total time for one cycle in hours = 45 minutes / 60 minutes/hour = 0.75 hours
Average hourly output = 1 cycle / Total time for one cycle in hours = 1 / 0.75 = 1.33 cycles/hour
Since each cycle produces 100 units of the packaged product (one component A and one component B), the average hourly output in terms of the number of units of the packaged product is:
Average hourly output = Average hourly output * Number of units per cycle = 1.33 cycles/hour * 100 units/cycle = 133 units/hour
Therefore, the average hourly output is 133 units of the packaged product.