(a) Since the utility function is linear with all the 3 variables, calculating the marginal utility becomes easy. According to the function, with every hour of Lecture Time (L.T.) U decreases by 35 units, i.e. M.U. for L.T. is -35.
(b) When the cost of text book increases by 10 euros, U decreases by 70 units which has to be made up for by increasing M.B. Therefore extra M.B. K(say)*17.5=70, or K=4. So there should be 4 mins of extra break time.
(c) MU for LT and C are decreasing and M.B is increasing. This should not be reasonable because in plain words, the more lecture time is there the less utility the students find in the lecture. Which means that students prefer short lectures with cheaper books and more breaks