
a Lagrange question
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 ?)

Re: a Lagrange question
What's the use, you are going to fail EC223 anyway. Indeed, gec223 = 80+3tec223 and tec223 ≤ 20, so gec223 ≤ 20. Also, what is 20ptec233?
More seriously, this is the wrong way to ask a math question. Apparently, you copied and pasted the text from some source without bothering to proofread it, improve or explain the notation. Why are people supposed to guess that in tec233, t denotes time and ec233 refers to the name of the course EC233? Is it suppose to be something like $\displaystyle t_{\text{EC233}}$? Next, which Lagrange theorem are you referring to? Do you mean the method of Lagrange multipliers? Last but not least, have you tried solving the problem? Have you looked at the solution of similar problems? What exactly is your difficulty?

Re: a Lagrange question
Interesting idea for a word problem, but unfortunately, the underlying math is difficult to decipher and seems to make no sense (as emakarov points out, your grade in EC223 can not go above 20, and I'm thinking the scale is 0 to 100).
In problems like this, when the equations are linear, the answer usually lies at the endpoints. Whichever class is more efficient in terms of grade points per hour studied, you study that until your grade is an A, then spend the rest of the time bringing up your grade in the other class.
And no, you can not necessarily conclude that you need to study more for the harder class. Think about it  it could be that you are failing that class anyway, so you might as well study for the easier class.
If only we could get estimates like this in real life.....
 Hollywood

Re: a Lagrange question
sorry for delay, I had two exam after posting this problem, so I can just get a chance to see the posts. when it comes to the questions, I also did not understand what pt.. is, but assumed that it is also t... and tried to solve the question. I found the average and maximized it with subject to t223+t233<=20. however, I could not get a result and I had no time to go into the problem deeply, so I posted the question here. now, I just wonder what is the problem of the way I thought about this problem? why can I not face with a solution?
and I named the thread as lagrange question because we are covering this part of calculus and the other questions are also about lagrange theorem. In addition, I tried to solve the question by using lagrange but how can solution be? thank for your help. maybe I cannot understand the question well, because I did not understand the lagrange theorem exactly.

Re: a Lagrange question
I think you must mean the method of Lagrange multipliers. If you use the terms that other people use, they are more likely to understand you. I'm sure there are many Lagrange theorems  Lagrange was a very influential mathematician. The Lagrange theorem I'm thinking of has nothing to do with your problem.
We still need a clear definition of the problem, but maybe that would come out if you show us what work you have done. Specifically, what stopped you from getting a result?
 Hollywood