This is a question from textbook "Algorithm Design" Chapter 6 Exercise 20

https://www.chegg.com/homework-help/Algorithm-Design-1st-edition-chapter-6-problem-20E-solution-9780321295354

Suppose it's nearing the end of the semester and you're taking n courses, each with a final project that still has to be done. Each project will be graded on the following scale: It will be assigned an integer number on a scale of 1 to g > 1, higher numbers being better grades.Your goal, of course, is to maximize your average grade on the n projects.

You have a total of H > n hours in which to work on the n projects cumulatively, and you want to decide how to divide up this time. For simplicity, assume H is a positive integer, and you'll spend an integer number of hours on each project. To figure out how best to divide up your time, you've come up with a set of functions {f_i : i = 1, 2, n)(rough estimates, of course) for each of your n courses; if you spend h < H hours on the project for course i, you'll get a grade of f_i(h). (You may assume that the functions f_i are nondecreasing: if h < h', then f_i(h) < f_i(h').)

So the problem is: Given these functions {f_i}, decide how many hours to spend on each project (in integer values only) so that your average grade, as computed according to the f_i, is as large as possible. In order to be efficient, the running time of your algorithm should be polynomial in n, g and H; none of these quantities should appear as an exponent in your running time