2. (3 points) Time management is often a difficult task. Usually Tim studies m hours per week. In this term, he has n courses and course i{1,,n} requires at minimum ki hours (e.g. going to classes, discussions). Assume there is a family of linear functions fi(x)=aix+bi with ai[0,) and biR, which estimate the expected score of the course i if Tim studies x hours per week for that course. How can Tim allocate his time per week so that he can achieve the maximum expected average score of the whole term? Write a linear program that solves this