SOLUTION
The problem is an issue of maximizing profit under constraints. First, we state the constraint equations.

Since the objective is to maximize profit, under constraint, we look for the book that yields the best profit for each weight. NOTE: the issue of weight is the biggest constraint being faced by BK

Profit per weight = (Sales Price – Cost price)/Weight

This method gives a ranking such that it tells the books that yield the largest profit per weight constraint.

Title Weight Cost Sale Price Profit Per Weight Ranking Harry Potter, JK Rowling 5 9 17 1.6 1 The Lord of the Rings, JRR Tolkien 4 8 13 1.3 2 Chronicles of Narnia, CS Lewis 3.5 7 11 1.1 3 A Series of Unfortunate Events, Lemony Snicket 3 6 9 1.0 4 A Wrinkle in Time, Madeleine L’Engle 1 4 5 1.0 4 Charlie and the Chocolate Factory, Roald Dahl 2.5 5 7 0.8 5
Since we have seen the rankings, we then know the ones to put more importance into to. Therefore, we have more chances of putting JK Rowling into the boxes above that of JRR Tolkien etc.

Remember we have a minimum of four books from each author and a minimum of three authors. These are not maximums so we have a lot of leverage here.

The maximum combination will be found at the absolute minimum of all books that can be selected. This is at 4, 4, 4 for JK Rowling, JRR Tolkien, and CS Lewis. This maximizes the reported profit while ensuring the non-violation of the constraint equations.

CONSTRAINT EQUATIONS
Let a. b, c, d, e, and f be the designations for JK Rowling, JRR Tolkien, CS Lewis, Lemony Snicket, Madeleine L’Engle, and Roahld Dahl respectively

Therefore

5a + 4b + 3.5c + 1d + 3e + 2.5f 4