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Determine Worker Counts from Production Ratios

BarclaysData Scientist · Online Assessment
EasyData ScientistOnline AssessmentStatistics & Math

Last updated

This problem tests mathematical modeling and systems of linear equations by requiring the candidate to derive specific headcount requirements based on production demand and individual productivity constraints.

Problem Statement

A furniture factory produces custom desks that require both steel nails and iron screws. The assembly process dictates that for every 2 nails used, exactly 1 screw must be used.

Each day, the factory must produce a volume of goods that consumes a total of 10,000 components (nails + screws combined).

Worker productivity is specialized:

  • A 'Nail-Specialist' worker can install 500 nails per day and 0 screws.
  • A 'Screw-Specialist' worker can install 250 screws per day and 0 nails.

Calculate the exact number of Nail-Specialists and Screw-Specialists required to meet the daily production quota of 10,000 components while maintaining the 2:1 ratio. Return the count of each worker type and the total number of workers as a tuple: (nail_workers, screw_workers, total_workers).

Constraints

  • The factory must operate with integer counts for each worker type.
  • The total number of components used must be exactly 10,000.
  • The ratio of nails to screws installed must be exactly 2:1.

Example

If the total components required were 300:

  • We need 200 nails and 100 screws to satisfy the 2:1 ratio.
  • Nail-Specialists needed: 200 / 500 = 0.4 (Wait, the components must be met exactly, so assume a smaller scale for the example).
  • For this problem, focus on the 10,000 component requirement.

Edge Cases

  • What if the daily component quota is not perfectly divisible by the individual worker outputs?
  • Ensure the solution handles the ratio constraint before the worker allocation.

Hints

Hint 1

First, determine the absolute number of nails and screws needed by dividing the 10,000 total components into parts based on the 2:1 ratio.

Hint 2

Once you have the total nails (2/3 of 10,000) and screws (1/3 of 10,000), divide these totals by the daily output per worker type.

Hint 3

Remember that the factory cannot hire fractional workers, so verify if the required counts result in whole numbers.

Follow-up questions

  • How would your calculations change if the ratio of nails to screws changed to 3:2?
  • If Nail-Specialists could also install 100 screws per day, how would that transform the system of equations?
  • What strategy would you propose if the daily component requirement fluctuated significantly, making fractional workers inevitable?