A student is taking two courses. They wish to maximise their average mark for the two courses. The marks they will get are functions of time. For both courses the marks functions are as follows: 1 M1 = 50 + at , where the time the student allocates to the first course is t;; -120 + Bt2 , where the time the student allocates to the second course is t2. M2 M1+M2 The average grade will be 2 G. The total time available for study is 80 hours Find the optimal time the student spends on studying each course, (a) in terms of a and ß. Do not check the second order conditions. (b) Hence find the optimal marks for each course, again in terms of a and B. (c) Now let a = 14 and ß = 2. What is the average mark achieved by this optimisation?
A student is taking two courses. They wish to maximise their average mark for the two courses. The marks they will get are functions of time. For both courses the marks functions are as follows: 1 M1 = 50 + at , where the time the student allocates to the first course is t;; -120 + Bt2 , where the time the student allocates to the second course is t2. M2 M1+M2 The average grade will be 2 G. The total time available for study is 80 hours Find the optimal time the student spends on studying each course, (a) in terms of a and ß. Do not check the second order conditions. (b) Hence find the optimal marks for each course, again in terms of a and B. (c) Now let a = 14 and ß = 2. What is the average mark achieved by this optimisation?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help solve question 11 A B and C as seen in picture attahced please show full working so I can understand.
Thank you
Transcribed Image Text:11.
A student is taking two courses. They wish to maximise their average mark for the two
courses.
The marks they will get are functions of time. For both courses the marks functions
are as follows:
1
M1
50 + at , where the time the student allocates to the first course is t;;
-120 + ßt2 , where the time the student allocates to the second course is
M2
t2.
M1+M2
The average grade will be
2
= G.
The total time available for study is 80 hours
(a)
Find the optimal time the student spends on studying each course,
in terms of a and B. Do not check the second order conditions.
(b)
Hence find the optimal marks for each course, again in terms of a and B.
(c)
Now let a = 14 and B = 2. What is the average mark achieved by this optimisation?
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