You are operating a web site to match up sellers and buyers of a product. 35 sellers and 35 buyers have input their reservation prices, as listed in the file P08_23.xlsx. For example, buyer 1 is...

You are operating a web site to match up sellers and buyers of a product. 35 sellers and 35 buyers have input their reservation prices, as listed in the file P08_23.xlsx. For example, buyer 1 is willing to pay up to $8 for an item, and seller 1 is willing to accept $9 or more for an item. This means that buyer 1 and seller 1 cannot be matched.

The goal of http://www.SplitTheDifference.com (there is such a Web site run by Yale professor Barry Nalebuff) is to pair buyers with sellers to maximize the sum of buyers’ and sellers’ surplus. For example, if buyer 31 and seller 31 are matched, a deal can be made by splitting the difference with a price of $57. Then buyer 31 earns a surplus of 60 – 57= $3, and seller 31 earns a surplus of 57 – 54= $3. What is the maximum sum of buyers’ and sellers’ surplus that can be obtained?