-Total production must be 100 units.

  Blog    |     February 16, 2026

The factory normally produces 50 units of Product A and 50 units of Product B on a standard day, totaling 100 units. On Audit Day, the factory misused the day by producing a different mix of products while still maintaining a total production of 100 units. The constraints for Audit Day production are:

  • At least 10 units of each product must be produced.
  • The production of Product A must exceed that of Product B (i.e., A > B).

Given these constraints, the production quantities on Audit Day that satisfy all conditions and represent the most extreme deviation from the normal mix (due to the misuse) are:

  • Product A: 90 units
  • Product B: 10 units

Explanation:

  • Total production: 90 + 10 = 100 units, meeting the total constraint.
  • Minimum production per product: Both A (90 ≥ 10) and B (10 ≥ 10) meet the minimum requirement.
  • A > B: 90 > 10, satisfying the condition that Product A production exceeds Product B.
  • Deviation from normal mix: The normal mix is 50A and 50B. The Audit Day mix (90A and 10B) is the most extreme possible under the constraints, as it maximizes Product A and minimizes Product B while still adhering to the rules. This significant shift constitutes misuse, as it deviates substantially from the standard production plan.

This solution highlights the factory's misuse of Audit Day by prioritizing one product over the other to an extreme degree, potentially indicating an attempt to meet specific targets or inefficiencies in production planning.


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