3. A processor makes two components, A and B, which are then packaged together as the final product (each product sold 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 times for each component are given below. 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)?

Component A – Setup/Charge over Time is 5 minutes and Run Time/Unit is 0.2 minutes
Component B – Setup/Charge over Time is 10 minutes and Run Time/Unit is 0.1 minutes

I am having a hard time with this one. I don't know where to begin.

What the question is saying is that the production line

1. sets up for producing product A (takes 5 minutes),
2. produces 100 units of A (100*0.2 minutes)
3. switches to produce product B (10 minutes setup)
4. produces 100 units of B (100*0.1 minutes).
This cycle produces 100 units of A and 100 units of B, which can then be packaged to 100 units of the final product.

How much time in minutes is required to produce 100 units?
- Add up the time required for steps 1 to 4 which is the time required to produce 100 units.

Conversely, how many units are produced in an hour (60 minutes?)

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To find the average hourly output, we need to calculate the time it takes to produce 100 units of each component and then divide it by the total time taken.

Let's begin by calculating the time taken for each cycle of producing 100 units of A and B:

Time for 100 units of A:
Setup time: 5 minutes
Run time: 0.2 minutes per unit
Total run time for 100 units: 0.2 * 100 = 20 minutes
Total time for component A: 5 + 20 = 25 minutes

Time for 100 units of B:
Setup time: 10 minutes
Run time: 0.1 minutes per unit
Total run time for 100 units: 0.1 * 100 = 10 minutes
Total time for component B: 10 + 10 = 20 minutes

Now, let's calculate the total time taken for each cycle, which includes both components A and B:

Total time per cycle = Time for component A + Time for component B
Total time per cycle = 25 minutes + 20 minutes = 45 minutes

To find the average hourly output, we need to calculate the number of cycles that can be completed in an hour:

Number of cycles per hour = 60 minutes / Total time per cycle
Number of cycles per hour = 60 minutes / 45 minutes = 4/3 cycles

Since each cycle produces 100 units of the packaged product (containing 1 A and 1 B), the average hourly output in terms of the number of packaged products is:

Average hourly output = Number of cycles per hour * Number of units per cycle
Average hourly output = (4/3) * 100 = 400/3 = 133.33 units

Therefore, the average hourly output would be approximately 133.33 units of the packaged product.

To calculate the average hourly output, you need to determine the total production time for each component and the total number of packaged products produced in an hour. Here's how you can approach it step by step:

1. Calculate the total production time for each component.
- For component A, you have a setup time of 5 minutes and a run time of 0.2 minutes per unit. Since you are making 100 units of component A, the total production time for component A can be calculated as follows:
Total Production Time for Component A = (Setup Time for Component A + (Run Time per Unit for Component A × Number of Units of Component A))
Total Production Time for Component A = (5 minutes + (0.2 minutes/unit × 100 units))
Total Production Time for Component A = (5 minutes + 20 minutes)
Total Production Time for Component A = 25 minutes

- For component B, you have a setup time of 10 minutes and a run time of 0.1 minutes per unit. Since you are making 100 units of component B, the total production time for component B can be calculated as follows:
Total Production Time for Component B = (Setup Time for Component B + (Run Time per Unit for Component B × Number of Units of Component B))
Total Production Time for Component B = (10 minutes + (0.1 minutes/unit × 100 units))
Total Production Time for Component B = (10 minutes + 10 minutes)
Total Production Time for Component B = 20 minutes

2. Determine the total number of packaged products produced in an hour.
- Since you are producing components A and B in alternating batches of 100 units each, you will have a cycle time of:
Cycle Time = Total Production Time for Component A + Total Production Time for Component B
Cycle Time = 25 minutes + 20 minutes
Cycle Time = 45 minutes

- To calculate the number of cycles completed in an hour, you need to convert the hour into minutes (since the cycle time is in minutes):
Number of Cycles per Hour = 60 minutes ÷ Cycle Time
Number of Cycles per Hour = 60 minutes ÷ 45 minutes
Number of Cycles per Hour = 1.33 cycles (rounded to 2 decimal places)

- As each cycle produces one packaged product containing one component A and one component B, the total number of packaged products produced in an hour can be calculated as:
Total Packaged Products per Hour = Number of Cycles per Hour × Number of Units per Cycle
Total Packaged Products per Hour = 1.33 cycles × 100 units per cycle
Total Packaged Products per Hour = 133.33 products (rounded to 2 decimal places)

Therefore, the average hourly output, in terms of the number of units of packaged products, is approximately 133.33 products.