Apply complex models and bottlenecks
Combine rates, resource limits and whole-item constraints before calculating output.
Original StudyForA scenarios and formative model answers; no Cambridge marks, predicted grades or certified mastery. Alternative reasoned answers may be valid. Full-length unseen papers, a wider mixed-problem bank and calibrated specialist teacher marking remain outstanding.
Before you begin
- Read tables and instructions in English
- Use arithmetic, ratios and whole-number constraints
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Before calculating, what should you identify?
What you will learn
- Apply interacting rules and capacity limits
- Identify which resource limits feasible output
Convert everything to a common time interval
A production system can have enough assembly capacity but too little finishing capacity. Find the capacity of each required stage, then use the minimum; adding the stage capacities would count items that have not completed the whole process.
A fictional workshop has two assemblers, each making 3 items an hour, and one finisher completing 4 items an hour. In five hours, assembly capacity is 30 and finishing capacity 20. With enough starting assembled stock or a model allowing continuous simultaneous flow, output is capped at 20 finished items.
Check what the model assumes
The capacity minimum is an upper bound. It is attained only if timing, starting stock and other constraints permit it. A job-by-job process starting empty can lose time while the first item reaches the next stage. State whether the problem uses continuous rates, complete batches or individual jobs.
For whole items, round capacity down when partial work cannot count as an output. Distinguish a resource ceiling from a schedule that actually meets it, especially in multi-part A Level problems.
Sources for this lesson
Pause and explain
Can adding an assembler raise output when finishing alone remains the bottleneck?
Worked example
Under the continuous-flow model with enough starting stock, find five-hour finished output.
Show the worked solution
- Assembly offers 2×3×5=30.
- Finishing offers 4×5=20.
- Every finished item needs both stages, so use the smaller capacity.
Answer The maximum is 20 finished items under the stated stock and flow assumptions. Finishing is the bottleneck; an extra assembler alone would not raise this limit.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Guided: Explain why the workshop cannot finish 30 items in five hours.
Give me a hint
Every item needs finishing.
Compare my reasoning
- Assembly can supply thirty.
- The finisher completes at most twenty.
- Ten assembled items cannot be counted as finished.
Thirty is assembly capacity only. Since all items require finishing and that stage can complete at most twenty, thirty finished items violate a necessary stage limit.
Look for these in your work
- Separates stages
- Uses the bottleneck
- Distinguishes finished output
Independent: Two parallel machines take 12 and 20 minutes per complete job. Both work for 60 minutes and need no shared resource. How many jobs finish?
Give me a hint
Round each machine’s capacity separately.
Compare my reasoning
- The first completes 60÷12=5 jobs.
- The second completes 60÷20=3.
- Add completed outputs from independent machines.
Eight jobs finish: five on the first machine and three on the second. Here addition is correct because each machine completes an independent whole job, unlike required sequential stages.
Look for these in your work
- Counts each capacity
- Uses whole jobs
- Explains why addition applies
Application: In the workshop, a second identical finisher is added. Under the same continuous-flow model, what is the new five-hour output limit?
Give me a hint
Recalculate both stages.
Compare my reasoning
- Assembly remains thirty.
- Finishing becomes 2×4×5=40.
- Take the smaller capacity.
The limit becomes 30 finished items, with assembly now the bottleneck. The extra finisher raises finishing capacity to forty, but cannot supply the missing assembled items.
Look for these in your work
- Updates only changed capacity
- Finds the new bottleneck
- States the model assumptions
Common mistakes
- Adding capacities of required stages
- Counting partial items as completed
- Ignoring startup or batch delays
What can you explain now?
Can adding an assembler raise output when finishing alone remains the bottleneck?
Compare with the explanation
No, the finishing capacity still limits output
A stage that is not limiting does not remove the active bottleneck.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Can adding an assembler raise output when finishing alone remains the bottleneck?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.