Allocate a constrained budget
Which combinations fit after reserving a safety margin?
Entering midway? Revisit Does twice the speed mean half the journey? for the preceding worked example, or start here and use the explanation below.
Start with a concrete question
An original synthetic project buys A units for 4 credits and B units for 6. Choose a reserve and A quantity, then calculate the maximum whole B quantity.
Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.
What do you expect?
Predict how one extra A changes the feasible B count.
Change one thing. Inspect what happens.
- At default settings calculate remaining funds before B.
- Increase A one unit at a time and explain the staircase in whole B units.
- Choose an infeasible A/reserve pair; explain why zero B does not make it feasible.
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Compare the current results
Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.Follow the calculation
- Budget 100 − reserve 20 − 10 A units × 4 = 40 credits for B.
- Each B costs 6; whole affordable units = max(0, floor(40/6)) = 6.
- Total committed = 20 + 40 + 36 = 96.
A constraint defines feasible choices. More of one item reduces room for another; negative availability signals an infeasible A/reserve choice.
Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.
Explain the mechanism
Allocate a constrained budget
An original synthetic project buys A units for 4 credits and B units for 6. Choose a reserve and A quantity, then calculate the maximum whole B quantity.
Predict before changing inputs
Predict how one extra A changes the feasible B count.
Understand the mechanism
A constraint is a rule every allowed choice must satisfy. Here 4A + 6B + reserve ≤ budget.
With 100 credits, 20 reserved and 10 A units, 40 remain. Six B units cost 36 and leave 4 credits.
Floor means the greatest whole number no larger than a value. You cannot buy 6.67 indivisible items.
Calculate it yourself
B = max(0, floor((budget − reserve − 4A)/6)), with feasibility checked separately.
Guided investigation
At default settings calculate remaining funds before B.
Increase A one unit at a time and explain the staircase in whole B units.
Choose an infeasible A/reserve pair; explain why zero B does not make it feasible.
Assumptions and limitations
Prices and quantities are fixed assumptions; no bulk discounts or utility ranking.
Feasible does not mean best: the value of each item is not modeled.
Further investigations
High school: Plan a fictional school event with an explicit contingency reserve.
College: Enumerate feasible integer choices and optimize a stated utility.
Working professionals: Document a resource-allocation decision and its sensitivity to cost changes.
Try a fresh case
Budget 90, reserve 10, and 8 A units at 4 each: how many whole B units at 6 fit?
This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.
Take the investigation further
Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.
School investigation
Plan a fictional school event with an explicit contingency reserve.
College investigation
Enumerate feasible integer choices and optimize a stated utility.
Workplace investigation
Document a resource-allocation decision and its sensitivity to cost changes.
Keep the evidence, choose your next step
Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.