Let a(t) represent the number of tumor cells at time t (with exponential grow factor a > 0), and u(t) the drug concentration. We wish to simultaneously minimize (a) the number of tumor cells at the end of the treatment period, (b) the accumulated harmful effects of the drug on the body, (c) the length of the treatment period. Thus the problem is formulated as T min {x{7} + [²" } -(0)9² de} u,T subject to (t) ax(t)u(t), x(0) = 7. Find the solution to this problem.
Let a(t) represent the number of tumor cells at time t (with exponential grow factor a > 0), and u(t) the drug concentration. We wish to simultaneously minimize (a) the number of tumor cells at the end of the treatment period, (b) the accumulated harmful effects of the drug on the body, (c) the length of the treatment period. Thus the problem is formulated as T min {x{7} + [²" } -(0)9² de} u,T subject to (t) ax(t)u(t), x(0) = 7. Find the solution to this problem.
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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Transcribed Image Text:Let z(t) represent the number of tumor cells at time t (with exponential grow factor a > 0), and u(t) the
drug concentration. We wish to simultaneously minimize
(a) the number of tumor cells at the end of the treatment period,
(b) the accumulated harmful effects of the drug on the body,
(c) the length of the treatment period.
Thus the problem is formulated as
min
1,T
£jn {x{7} + [²" }{4{!}² d²}
(T)
zu(t)²
dt
subject to
i(t)
ax(t)u(t), x(0) = 7.
Find the solution to this problem.
=
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