Consider the following three-letter words: AFT, FAR, TVA, ADV, JOE, FIN, OSF, and KEN. A letter is assigned a code starting with A = 1 and ending with Z = 26. Each word is scored by adding numeric codes of its three letters. For example, AFT has a score of 1 + 6 + 20 = 27. The goal is to select five of the given eight words that yield the maximum total score. Simultaneously, the selected five words must satisfy the following conditions:

Formulate the problem as an ILP, and find the optimum solution.

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sum of letter 1 scores } < (² sum of letter 2 scores } <[ sum of letter 3 scores