Answered: A certain dosage of radiation, measured…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

A certain dosage of radiation, measured in kilorads, must be given to the tumor near the brain. The dose delivered must be sufficient to kill the malignant cells but the aggregate dose must not exceed established tolerance levels for the brain. Two beams which would deliver radiation exposure to the cells will be used. The goal is to select certain beam durations that would generate the best dosage distribution by minimizing the radiation absorbed by the brain. The data for the radiation therapy is given below:

a. Define the variable used:

b. LP Model:

c. Identify the feasible region

d. Corner Points and the objective functions:

e. Optimal Solution (final answer):

Fraction of dose absorbed per second
Average dosage
Area
Beam 1
Beam 2
(in kilorads)
Brain
0.4
0.5
Spine
DIFIC
0.3
0.1
At most 2.7
Tumor
0.5
0.5
At most 6
191
0.6
Center of Tumor
0.4
At least 6
GUT
Determine the optimal exposure times for beam 1 and beam 2.
SPIENT

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