A processor makes two components, A and B, which are then packaged together as the final product (each product sold contains one A and 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, etc, where the setup and run times for each component are given below.

Component setup/Change over time Run time/unit
A 5 minutes 0.2 minute
B 10 minutes 0.1 minute

Assume the packing of the two components is totally automated and is small enough that you can ignore it. What is the average hourly output, in terms of the number of units of packaged product (which includes one component A and one component B)?

Total time required to produce 100 units of A is equal to Component setup time/Change over for A plus basic time required to produce 100 units of A. Therefore,

Total time required to produce 100 units of A = 5 minutes + 20 minutes

= 25 minutes

2. Calculation of time to produce 100 units of B

Component setup time/Change over for B = 10 minutes

Basic time required to produce 100 units of B = B's run time/unit × 100

= 0.1 minute × 100

= 10 minutes

Total time required to produce 100 units of B is equal to Component setup time/Change over for B plus basic time required to produce 100 units of B. Therefore,

Total time required to produce 100 units of B = 10 minutes + 10 minutes

= 20 minutes

3. Calculation of total time required to produce 100 packages that contains one component A and one component B each (Time for 100 packages)

Total time required to produce 100 packages that contains one component A and one component B each (Time for 100 packages) is the addition of total time required to produce 100 units of A and total time required to produce 100 units of B. This is given as follows:

Time for 100 packages = 25 minutes + 20 minutes

= 45 minutes

Since, there is only 60 minutes in one hour and 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, etc with each 100 units requiring at least 20 minutes, only an average of 100 packages which includes one component A and one component B each can be produced per hour. This is because, the 15 minutes left after using 45 minutes from 60 minutes in one hour can not be enough to another 100 packages using the current plan.

All the best.