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…

Answered: 1. Formulate a linear program to…

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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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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I have collected real data on the sale of a microwavable cup of soup across 20 different cities for the same time period (a month). The variables in the dataset are: Quantity sold in the city for that month: Measured in thousands of units Price: measured in dollars Average Income in the city: Measured in thousands of dollars Ads: Average number of ads run in stores for that city during that month. Price of a substitute product: measured in dollars Population of the city: measured in thousands of people The dataset is on Canvas and, using Excel or any other statistical software, please answer the following questions: 1. Describe the patterns in quantity sold and own and rival prices during this time period using basic descriptive statistics. Graphs are welcome as well. 2. Take the logs of the variables, and estimate the demand function. a. Interpret the R-square. b. Interpret the coefficients for logP and logPsub c. Interpret the p-values associated with each independent…
1. Instruction: For each of the following variables, indicate whether it is qualitative or quantitative. For quantitative variables, further categorize them into the discrete or continuous type. (a) Gender (b) Hospital bed capacity. (c) Blood glucose level (in mg/100 mL) (d) Systolic blood pressure (e) Height (in centimeter) (f) Blood type (g) Per capita income (h) Household size (i) Mid-upper arm circumference (in centimeter) () Region (k) Pulse rate (I) Civil status
Region Product Type Item Projected Sales 2022 (in millions) Americas Legacy B 18.6 Americas Legacy B 1.4 Americas Legacy B 9.4 Americas Legacy B 11.6 Americas Legacy B 7.1 Americas Legacy B 8.6 Americas Legacy B 6.9 Americas Legacy B 9.4 Americas Legacy B 8 Americas Legacy B 12.4 Americas Legacy B 16.3 Americas Legacy B 12.4 Americas Legacy B 5.7 Americas Legacy B 8.1 Americas Legacy B 14.6 Americas Legacy B 3.2 Americas Legacy B 13.1 Americas Legacy B 6.5 Americas Legacy B 6.6 Americas Legacy B 14 Americas Legacy B -1.6 Americas Legacy B -5.5 Americas Legacy B 10.5 Americas Legacy B 9.7 Americas Legacy B 5.9 Americas Legacy B 9 Americas Legacy B 7.9 Americas Legacy B 4.4 Americas Legacy B 8.2 Americas Legacy B 2.9 Americas Legacy B 10.6 Americas Legacy B 7.8 Americas Legacy B 5.2 Americas Legacy B 14.4 Americas Legacy B 4.1 Americas Legacy B 7.7 Americas Legacy B 2.6 Americas Legacy B 10.1 Americas Legacy B…
1. Estimate the retails sales in the U. S. in 2011. billions of dollars = 2. Use the model to predict the year that corresponds to retails sales of $249 billion =
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Price elasticity of demand (supply) or simply elasticity of demand (supply) measures the relative or percentage variation experienced by the quantity demanded (supplied) as a consequence of a change in the price of one percent (1%); In other words, it measures the intensity with which buyers (sellers) respond to a change in the priceprice. Elasticity is often used with respect to the price-demand relationship or the price-supply relationship, but the applicability of this concept is not restricted to that single case, but is broader, since the elasticity is calculated in percentages, since it is the only way to obtain a common unit of measure. When calculating the elasticity in arelationship, the units of measurement are maintained, therefore, they do not measure a proportional change, but a propensity, such as the well-known propensit to Keynesian consumption. The rate at which the selling price changes and from a product, with respect to its supply "x", is given by the following…
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An automobile manufacturer is considering mechanical design changes in one of its top-selling cars to reduce the weight of the car by at least 420 pounds to improve its fuel efficiency. Design engineers have identified 10 changes that could be made in the car to make it lighter (e.g., using composite body pieces rather than metal). The weight saved by each design change and the estimated costs of implementing each change are summarized in the following table. Design Change 1 2 3 4 6 7 8 10 Weight Saved (Ibs) 50 75 25 150 60 95 200 40 80 30 Cost (in $1,000s) 150 350 50 650 90 35 450 75 110 30 Changes 4 and 7 represent alternate ways of modifying the engine block and, therefore, only one of these options could be selected. The company wants to determine which changes to make in order to reduce the total weight of the car by at least 420 pounds in the least costly manner. (a) Formulate an ILP model for this problem to minimize cost (in thousands of dollars). (Let X, = 1 if design change i…
We have data on the lean body mass and resting metabolic rate for 12 women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person's weight leaving out all fat. Metabolic rate, in calories burned per 24 hours, is the rate at which the body consumes energy. Mass 40.5 37.9 54 50.8 48.9 51.9 52.3 36.7 37.3 44.7 37.6 46.7 Rate 1380 1560 980 1170 1230 1240 1480 1560 1440 1130 1570 1490 Find the least-squares regression line for predicting metabolic rate from body mass.ANSWER: y^=