What to automate first · Scoring

The cost of a mis-sent quote

Price three kinds of wrong quote from a 200-request replay, cost a two-minute check against them, and decide whether quotes may go out unchecked.

estimatehardExercise · 3 min · 10 of 75

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A prototype quotes correctly 188 times in 200. Whether it may send quotes on its own depends on what the other 12 cost, and they do not all cost the same.

The situation

The agency sells three fixed-price website packages, quoted from a web form: 60 requests a month, 12 minutes each for an account manager at an assumed $30 an hour. A prototype workflow picks the package and add-ons from the form's fields and fills the quote; a model reads the form's free-text box. Replayed on 200 past requests, it matched the quote actually sent 188 times. Of the 12 misses, 7 were underpriced, an add-on left out, by $900 on average; 4 were overpriced, the wrong package; 1 carried another client's name and prices in its header.

Assume 30% of quotes are accepted, and an accepted underpriced quote is honoured. An overpriced quote loses half the deals it would have won, and a won project carries $2,400 of margin. A quote showing another client's prices costs the agency that other client one time in four, at $8,000 of margin. A 2-minute check by the account manager catches 9 errors in 10.

The question

Estimate the monthly cost of mis-sent quotes with no check and with the 2-minute check, and decide whether quotes may go out unchecked.

A strong answer · Rubric · Where answers go wrong

Write your answer first, then open

A strong answer

The replay's rates on 60 quotes a month: underpriced 60 × 7/200 = 2.1, overpriced 60 × 4/200 = 1.2, wrong client 60 × 1/200 = 0.3.

Each class has its own chain:

underpriced: 2.1 × 30% accepted × $900 = $567
overpriced: 1.2 × 30% × 50% lost × $2,400 = $432
wrong client: 0.3 × 25% × $8,000 = $600

Unchecked, about $1,600 a month: roughly $440 a miss, tolerance 3 on the scoring frame, not the 5 that "94% accurate" suggests.

Checked: 60 × 2 min = 2 hours × $30 = $60, and one error in ten survives, $160. About $220 against $1,600, so quotes do not go out unchecked.

The wrong-client miss is a template defect, not a judgement. Refuse to send any quote whose header name differs from the form's: that removes the $600 line for no minutes. Unchecked then costs about $1,000; checked, $60 + $100 = $160.

The automation still pays with the check in it: by hand is 60 × 12 min = 12 hours, $360 a month, against about $160 plus a small run cost.

Decision: build the name check first, and every quote gets the 2-minute check. The check pays while it prevents more than $60 a month. A mispriced quote averages about $300 of expected loss ($270 underpriced, $360 overpriced), so the line is $60 ÷ (90% × $300) ≈ 0.22 mispriced quotes a month, one in 270. A replay of 600 requests with two or fewer mispriced would reverse the decision.

Rubric

converts the replay's 12 misses into a monthly count per class
prices each class with its own chain of probabilities, not one average
prices the check both as minutes and as the errors it lets through
states the decision from the comparison
treats the wrong-client miss as a deterministic fix outside the check
names the error rate at which the check stops paying

Where answers go wrong

"94% accurate, so send them unchecked." Six percent of 60 is 3.6 misses a month and about $1,600; an accuracy figure means nothing until each kind of miss has a price.

"Every miss costs $900." This prices the overpriced quotes as if they were honoured and misses the $8,000 tail. The total is wrong, and the cheapest fix, the name check, never appears.

"The check takes an account manager's time, so it costs more than it saves." It is 2 hours a month, $60, against about $1,400 of losses it removes. The lesson on the arithmetic of a task prices a check the same way.