$[10$ points$]$ Assume there are $n$ buyers making offers $b_1,$dots,$b_n$ for some items, and there are $n$ sellers wishing to get

the amount $s_1,$dots,$s_n.$ 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$).$Assume there are n buyers making offers b$\_(1).....$b$\_($n$)$ for some items, and there are n sellers wishing to get the amount s$\_(1)....$s$\_($n$).$ 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:

a$.$Find the offer and the selling value with the minimum difference. Match this offer to the selling amount. Repeat until every offer is matched.

b$.$ Sort the buying offers and sort the selling targets. Match the smallest offer to the smallest target value according to the sorting, and repeat.

c$.$ One of these strategies is optimal. Give a counterexample for the wrong one and argue about the optimality of the other one.

I need $100\%$ correct and typed solution. Plz no scam or Ai or copied solution.