1. Formulate a linear program to minimize the total dose to the entire healthy anatomy. Consider the following problem in radiation therapy. Radiation therapy involves using an external beamtreatment machine to pass ionizing radiation through the patients body, damaging both cancerous andhealthy tissues. Our goal is to have enough radiation dosage throughout tumor region while keep thedamage to health tissues within a certain threshold. We consider a simplified case as follows. The tablebelow shows the fraction of dosage amount delivered to different areas by two beams.AreaHealth anatomyCritical tissuesTumor regionCenter of the tumorFraction (dose) of Beam 1absorbed by the area0.50.70.40.8Fraction (dose) of Beam 2absorbed by area0.50.30.60.2Suppose we are required to limit dosage reaching to critical tissues by b₁, and we want to send exactly b₂dosage amount to tumor region and at least b3 dosage amount to center of tumor.

Given,AreaFraction (dose) of Beam 1 absorbed by the areaFraction (dose) of Beam 2 absorbed by…

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1. Formulate a linear program to minimize the total dose to the entire healthy anatomy.

A First Course in Probability (10th Edition)

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1. Formulate a linear program to minimize the total dose to the entire healthy anatomy.

Consider the following problem in radiation therapy. Radiation therapy involves using an external beam
treatment machine to pass ionizing radiation through the patients body, damaging both cancerous and
healthy tissues. Our goal is to have enough radiation dosage throughout tumor region while keep the
damage to health tissues within a certain threshold. We consider a simplified case as follows. The table
below shows the fraction of dosage amount delivered to different areas by two beams.
Area
Health anatomy
Critical tissues
Tumor region
Center of the tumor
Fraction (dose) of Beam 1
absorbed by the area
0.5
0.7
0.4
0.8
Fraction (dose) of Beam 2
absorbed by area
0.5
0.3
0.6
0.2
Suppose we are required to limit dosage reaching to critical tissues by b₁, and we want to send exactly b₂
dosage amount to tumor region and at least b3 dosage amount to center of tumor.

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