I have a question about lagrange theorem and I need your help. thanks a lot.

You are preparing for the midterm exams of EC223 and EC233. You estimate that the grades you will obtain

in each course, as a function of the amount of time spent working on them are gec233 = 20 + 20ptec233

gec223 = −80+3tec223 where gi is the grade in course i and ti is the number of hours per week spent in studying

for course i. You wish to maximize your grade average (gec223 + gec233)/2. You cannot spend in total more

than 20 hours studying these courses in the week (perhaps because of the extra burden of EC205 on your poor

shoulders?). Find the optimal values of tec223 andtec233 and discuss the characteristics of the solution. (Since

EC233 is a harder course, can you expect tec233 > tec223 ?)