TOMORROW'S PRODUCTION. TODAY'S TRADEOFFS.
Make every minute count.
Fictional bakery; synthetic assumptions.
Learn why whole batches change the answer, and why a busy resource is not always worth expanding.
Edit operating assumptions
Solve applies these assumptions together. Editing clears the old allocation; capacity experiments use separate local solves. Reload resets the bakery; copy the solved rationale before leaving.
01 / SET THE OPERATING ASSUMPTIONS
A plan starts with the constraints.
02 / THE PRODUCTION DECISION
Finding the best feasible mix…
WHOLE BATCHES · 12 BOXES EACH
Your allocation.
| Product | Batches | Boxes | Contribution | Bound status |
|---|
If multiple mixes tie, the solver may return any optimum. There is no hidden customer priority.
WHERE THE DAY FILLS UP
Capacity, accounted for.
| Resource | Used | Available | Slack |
|---|
Zero slack means the resource is fully used. Compare actual extra-capacity solves below to learn what more minutes would earn.
THE VALUE OF CAPACITY
What would one extra hour earn?
Each result re-solves the whole-batch model with only that resource increased. Gross contribution gain excludes the cost of buying capacity; it is a finite experiment, not a price valid for every additional minute.
The two-product feasible region.
Scroll the diagram horizontally when needed. The exact constraints and coordinates follow it.
Fractional batches and manual comparison
03 / CHALLENGE THE RECOMMENDATION
What about your mix?
Check a manual allocation against the solved assumptions. It never replaces the recommendation.
THE FRACTIONAL COMPARISON
A bound, not a baking plan.
Why rounding an LP can fail
A continuous linear program (LP) allows partial batches. Its optimal contribution is an upper bound on the whole-batch model. Rounding each quantity independently can overspend capacity or miss commitments.
In the two-product lesson, the LP assigns 8/3 batches to each active product for $24. Rounding to 3 and 3 uses 9 prep and 9 oven minutes against 8 available. The true integer optimum is 3 and 2 batches for $23.
Each batch still contains 12 boxes. Whole-batch production is a planning policy; a fractional solution is not an instruction to make partial batches.
BRING THE ASSUMPTIONS WITH YOU
Take the rationale to the team.
Copy the allocation, resource accounting and all solved coefficients before leaving. Reload restores the example; the app saves nothing.
Model assumptions and limits
WHAT THE MODEL KNOWS
Precise arithmetic. Limited assumptions.
Contribution, not total profit.
The objective sums batches × contribution after variable costs. Fixed overhead, taxes and financing are outside this worksheet. Negative contribution can still be required by a minimum commitment.
One day, with known coefficients.
Resource use and contribution are linear and fixed. Demand is an assumed maximum, not a forecast distribution or guaranteed sell-through. Oven minutes are additive total use; they do not represent simultaneous trays or a sequenced oven. A feasible allocation is not a timed production schedule. This screen omits sequencing, spoilage, overtime tiers and uncertainty. Minimum commitments are explicit; the model invents no fairness rule.
The answer depends on the inputs.
All defaults are invented for class discussion. A binding resource alone does not identify a unique business cause or justify investment. Test alternatives and validate the assumptions before a real decision.
Local and reproducible.
HiGHS solves locally in a browser worker with a five-second limit per solve. The displayed plan is checked against the constraints and accounting. Changes clear old results. Nothing is uploaded or saved; reloading starts the bakery defaults.