Lorianne is studying for two different exams. Because of the nature of courses, the measure of study effectiveness on a scale from 0-10 for the first course is E1 = 0.6 [ 9 + te^(-t/20)], while the measure for the second course is E2 = 0.5 [ 10 + te^(-t/10)]. Lorianne is prepared to spend up to 30h in total studying for exams. The total effectiveness is given by f(t) = E1 + E2. How much time should be allocated to each exam to maximize total effectiveness.

The answer is suppose to be 10 hours and 20 hours.

I differentiated E1 + E2 and got the wrong answer.

Question

Lorianne is studying for two different exams. Because of the nature of courses, the measure of study effectiveness on a scale from 0-10 for the first course is E1 = 0.6 [ 9 + te^(-t/20)], while the measure for the second course is E2 = 0.5 [ 10 + te^(-t/10)]. Lorianne is prepared to spend up to 30h in total studying for exams. The total effectiveness is given by f(t) = E1 + E2. How much time should be allocated to each exam to maximize total effectiveness. 


The answer is suppose to be 10 hours and 20 hours. 

I differentiated E1 + E2 and got the wrong answer.