Question

Consider then the components of these problems that are itemized. For each of these components, identify whether it belongs to the data, the variables, the constraints or the objectives.

Cancer Treatment: There are different types of radiation machines that are used in the treatment of cancer. Some of them (like IMRT) consist of an “arm” that can rotate around the patient to help hit the tumor from different angles. The intensity of the laser beam can be adjusted at will. The beam is typically 10 cm² large and is made of adjustable beamlets of size 0.1 cm². A treatment plan needs to have the following characteristics to be applied: (1) the radiation dose on healthy tissue cannot be too large, (2) the radiation dose on targets cannot be too small. Moreover the treatment plan needs to make the radiation dose on sick tissue as large as possible and make the radiation dose on healthy tissue as small as possible.

(a) Angle of the arm to administer radiation.

(b) Beam size is 10 cm².

(c) Dose on sick tissue cannot be too small.

(d) Intensity of the beam.

(e) Dose on healthy tissue cannot be too large.

(f) Make the radiation dose on healthy tissue as small as possible.

Answer 1

We know ,

Data is information given to us,

Variable is a factor that is liable to vary,

Constraint is something that fix restriction,

And objective is what we have to achieve.

So according to this,

a) Angle of the arm to administer radiation is VARIABLE (as it can rotate at different angles).

b) Beam size (which is 10 cm2) is DATA.

c) The restriction that the dose on sick tissues can't be too small is CONSTRAINT.

d) Intensity of the beam is VARIABLE (because it is given that intensity can be adjusted at will).

e) The restriction that the dose on healthy tissues can't be too large is CONSTRAINT.

f) To make the radiation dose on healthy tissues as small as posiible is our OBJECTIVE.