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Let x(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 the number of tumor cells at the end of the treatment period and the accumulated harmful effects of the drug on the body and the length of the treatment period. So the problem is min (T)+(t)² dt subject to (t) = ax(t) u(t), r(0) = 7.

Let x(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 the number of tumor cells at the end of the treatment period and the accumulated harmful effects of the drug on the body and the length of the treatment period. So the problem is min (T)+(t)² dt subject to (t) = ax(t) u(t), r(0) = 7.

Advanced Engineering Mathematics
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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Let x(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 the number of tumor cells at the end of the treatment period and the accumulated harmful effects of the drug on the body and the length of the treatment period. So the problem is min (T)+(t)² dt subject to (t) = ax(t) u(t), r(0) = 7.
Transcribed Image Text:Let x(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 the number of tumor cells at the end of the treatment period and the accumulated harmful effects of the drug on the body and the length of the treatment period. So the problem is min (T)+(t)² dt subject to (t) = ax(t) u(t), r(0) = 7.
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