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This is a very calculation based question. How can someone do this in 2 mins?
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This is a very calculation based question. How can someone do this in 2 mins?
Actually, this question isn’t as calculation heavy as it looks. The key is to know when to calculate, what to calculate, and how precisely to calculate.

We only need to identify who earns more than 200 points (incentivized) and who earns less than 150 points (penalized). Instead of calculating for everyone, focus on extremes:

  • The worker with high production and few defects will likely cross 200.
  • The worker with low production and many defects will likely fall below 150.

Right away, Steve is the best candidate for being incentivized. He has high Type A and Type B output and very few defects. His positive points are roughly 50*3 + 40*2 = about 230. He has 11 total defects, and even if each defect were -1 point (which is more than the actual penalties), that’s only -11 overall. So his total would still be around 219, easily above 200.

For the penalized case, Hector stands out. He has much lower production and a large number of defects. His positive points are about 28*3 + 48*2 = 180. His negative points are large: 27 spoilage gives roughly -20, 19 major defects about -10, and 7 minor defects about -1.5, totaling slightly over -30. That brings his score to below 150, so Hector is clearly penalized.

The point is, you don’t need exact arithmetic here. You can quickly estimate, spot who’s at the top and bottom, and confirm only those two.
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Before doing any extra calculation, compare No-defect and Defects to choose most potential for highest points and for lowest points. Skim on structure and keep just numbers, weights are the same for all workers so higher quant = more points (added or deducted):

A+B+Spoil-Major-Minor-
Steve5342632
Mohan621616912
Hector284827197
Joseph294926187
Peter4041632
  • Up
  • Down

Top choices: Steave - Peter - Mohan

  • Steve: roughly 50*3 + 40*2 already passes 200 points, least defects (same amounts as Peter, much higher no-defect) - Steve wins
  • Mohan: roughly 60*3 + 20*2 also passes 200 points, however, lower than Steve, more defects than Steve - Steve wins

Bottom choices: Hector or Joseph
  • Hector must be lower: fewer no defects, higher defects

At this point we can do careful calculation to confirm our answer choices (to feel safe).
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"for incentives one must earn more points and loose less points and vice versa for penalty"
just looking at the choices:
for incentive: Steve and Mohan must be compared , but clearly Steve earns points by a far margin than Mohan however loses less so, Steve is the correct choice for incentive
for penalty: Hector and Joseph seems comparable, but clearly Hector earns five points less than Joseph but loses more points than him so, Hector is correct choice for penalty
(no need to get into tedious calculations)
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