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Realized profit by matching

Market makingMedium

A market maker buys $10$ units at $100$ , then buys $10$ units at $104$ , then sells $12$ units at $107$ . Sales are matched against the oldest purchases first. What is the realized profit?

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Hint

Match the sale against the first lot, then the remainder against the second lot.

Solution

The first $10$ sold are matched to the lot bought at $100$ and earn $10 \times (107 - 100) = 70$ .
The other $2$ sold are matched to the lot bought at $104$ and earn $2 \times (107 - 104) = 6$ .
The realized profit is $70 + 6 = 76$ .

Answer: $76$

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