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[ 1 0 points ] Assume there are n buyers making offers b 1 , dots, b n for some items, and there are n

[10 points] Assume there are n buyers making offers b1,dots,bn for some items, and there are n sellers wishing to get
the amount s1,dots,sn. Your goal is to match a buyer with a seller such that the total sum of all differences |b-s|
between the offer b and their assigned target value s is minimized. For example, assume you have two offers with
values 3 and 5, and two target amounts of 1 and 4. If you match 3 with 1 and 5 with 4, the total sum is |3-1|+|5-4|
=2+1=3. However, if you match them the other way around, the cost will be |3-4|+|5-1|=1+4=5. Hence the first
solution is more preferable.
Consider the following two greedy strategies:
Find the offer and the selling value with the minimum difference. Match this offer to the selling amount. Repeat
until every offer is matched.
Sort the buying offers and sort the selling targets. Match the smallest offer to the smallest target value according
to the sorting, and repeat.
One of these strategies is optimal. Give a counterexample (5pts for the wrong one and argue about the optimality
of the other one (5 pts).
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