Adapt solutions when conditions change
Identify which parts of a solution remain valid and recompute the parts affected by a new constraint.
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
- Trace the effects of changed conditions
- Recheck feasibility and optimality after a change
Change one rule and trace its consequences
A changed input can alter several outputs. Separate unchanged facts from changed ones before recalculating. Reusing earlier work is efficient only when its assumptions and dependencies still hold; a price change may preserve capacity while changing the cheapest plan.
Two-hour machine capacity is six complete jobs when each takes twenty minutes. If an unavoidable fifteen-minute setup is introduced, only 105 productive minutes remain, so capacity falls to five. The sixth job needs 120 productive minutes and no longer fits.
Check boundaries and knock-on effects
Integer capacities often change discontinuously. A small delay near a boundary can remove a whole job or connection. In schedules, propagate a delay through dependent tasks, while independent tasks may be unaffected.
Explain what changed and why the result follows. If several parameters change, do not blame the outcome on only one without isolating its contribution. Treat a new optimum as a fresh comparison, even when the old plan is still feasible.
Sources for this lesson
Pause and explain
How many complete twenty-minute jobs fit in 105 productive minutes?
Worked example
Recalculate the two-hour capacity after the fifteen-minute setup.
Show the worked solution
- Subtract setup: 120−15=105 minutes.
- Five jobs require 100 productive minutes.
- Six require 120, exceeding the available 105.
Answer The maximum falls from six to five complete jobs. Five is feasible, and the next possible whole-job count is excluded by the time bound.
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: How much unused productive time remains after five jobs?
Give me a hint
Compare available time with used time.
Compare my reasoning
- Five jobs use 100 minutes.
- Available productive time is 105.
- Subtract used from available.
Five productive minutes remain. They cannot produce another complete twenty-minute job, so the capacity remains five.
Look for these in your work
- Uses productive time
- Finds the remainder
- Preserves whole-job counting
Independent: The setup is reduced to zero but each job now takes 22 minutes. Find two-hour complete-job capacity.
Give me a hint
Test the last feasible and first infeasible count.
Compare my reasoning
- Five jobs take 110 minutes.
- Six take 132.
- 120 lies between these totals.
Five jobs finish in two hours, leaving ten minutes. The sixth would require 132 minutes, so removing setup does not restore the original six-job output when job duration also increases.
Look for these in your work
- Uses the changed duration
- Checks both counts
- Explains the outcome
Application: A trip originally arrives at 09:35 with a ten-minute walk before a 09:45 meeting. A diversion adds six minutes. Reassess the plan.
Give me a hint
Carry the delay through the dependent walk.
Compare my reasoning
- Stop arrival becomes 09:41.
- Venue arrival becomes 09:51.
- Compare with the unchanged deadline.
The plan now arrives six minutes late. The original exact-deadline solution had no spare time, so all six minutes propagate to the venue arrival.
Look for these in your work
- Updates arrival
- Includes the dependent task
- Rechecks the deadline
Common mistakes
- Keeping an old answer after a changed condition
- Forgetting downstream dependencies
- Rounding a whole-job capacity upward
What can you explain now?
How many complete twenty-minute jobs fit in 105 productive minutes?
Compare with the explanation
Five
Six requires 120 minutes; partial work does not count as a complete job.
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Make it stick
How many complete twenty-minute jobs fit in 105 productive minutes?
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.