Turn a production plan into resource needs
How can one table calculate several resource totals?
Entering midway? Revisit Reverse a probability question for the preceding worked example, or start here and use the explanation below.
Start with a concrete question
Original synthetic production: a small kit uses 2 kg material and 1 labor hour; a large kit uses 5 kg and 2 hours. Matrix rows represent resources.
Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.
What do you expect?
Predict which resource increases by more when one large kit replaces one small kit.
Change one thing. Inspect what happens.
- Compute both row totals for four small and three large kits.
- Replace one small kit with one large kit and inspect each unit.
- Choose a plan that exceeds material capacity; explain why labor cannot simply be subtracted from kilograms.
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
- Production vector = [4 small, 3 large].
- Resource matrix rows are material [2,5] and labor [1,2].
- Material row dot production = 2 × 4 + 5 × 3 = 23 kg.
- Labor row dot production = 1 × 4 + 2 × 3 = 10 hours.
A matrix applies several linear resource rules at once. Check row units before adding or comparing quantities.
Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.
Explain the mechanism
Turn a production plan into resource needs
Original synthetic production: a small kit uses 2 kg material and 1 labor hour; a large kit uses 5 kg and 2 hours. Matrix rows represent resources.
Predict before changing inputs
Predict which resource increases by more when one large kit replaces one small kit.
Understand the mechanism
A vector is an ordered list. The production vector has two entries: small-kit count and large-kit count.
A matrix is a table of coefficients. Multiplying each row by the production vector gives one resource total: material 2×4+5×3=23 kg, labor 1×4+2×3=10 hours.
Order and dimensions matter. A 2×2 resource matrix maps a 2-entry production vector to a 2-entry resource vector.
Calculate it yourself
[material, labor]ᵀ = [[2,5],[1,2]] × [small, large]ᵀ.
Guided investigation
Compute both row totals for four small and three large kits.
Replace one small kit with one large kit and inspect each unit.
Choose a plan that exceeds material capacity; explain why labor cannot simply be subtracted from kilograms.
Assumptions and limitations
Linear resource rates ignore setup costs, waste, overtime and learning effects.
Capacity checks cover material only; meeting it does not prove full production feasibility.
Further investigations
High school: Create a resource table for two meal types and compute totals.
College: Implement matrix multiplication with shape and unit checks.
Working professionals: Build a capacity proposal with explicit labor and material constraints.
Try a fresh case
A different workshop uses material coefficients [3,4]. For 2 small and 5 large products, how many kg are needed?
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
Create a resource table for two meal types and compute totals.
College investigation
Implement matrix multiplication with shape and unit checks.
Workplace investigation
Build a capacity proposal with explicit labor and material constraints.
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.