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…

Math

Probability

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...

See similar textbooks

Related questions

Q: A multiple regression analysis based on a data set that consists of 30 observations yielded the…

A: Given: P = $1000 I = $20000 A = $5000

Q: 1. Is it possible for a process be in control and still produce nonconforming output. Explain. What…

A: Nonconforming output A nonconforming output when not identified or controlled can lead to several…

Q: Many manufacturing situations, for example, the production of such large and complex items as…

A: Let x=Unit and y=Production hours x y 1 3211 2 2720 3 2615 4 2278 5 2028 6 2193 7…

Q: The table below contains price-demand and total cost data for the production of treadmills, where p…

A: Given, that a table contains price demand and the total cost data for the production of treadmills.…

Q: What are the characteristics of capital expenditures, and how do they vary from operating…

A: Capital expenditures : Long term expenses Operating expenditures : Short term expenses (day to…

Q: 1 NitrateLevel 2 50.1 3 48 4 46 5 45.9 6. 39.9 7 52.1

A: Answer: (a) (i) 44.52 confidence interval 95.% lower 48.42 confidence interval 95.% upper…

Q: Treatment Groups Auditory Tactile Visual 20-29 490 615 600 30-39 465 375 520 40-49 685 500 605 50-59…

A: As per guidelines we will solve the first question only, please repost other questions for more…

Q: 1. Complete the table Po P - value а. 100 40/100 8% b. 248 51/248 10% C. 312 100/312 12% d. 486…

A: See the handwritten solution

Q: . A farmer has recently acquired a 50 hectares piece of land. He has decided to grow corn and banana…

A: To formulate a linear programming problem for the given situation.

Q: It is believed that large doses of acetaminophen (the active ingredient in over the counter pain…

A: Given that Margin of error =E =0.03 98% confidence interval.

Q: 4. At Jalisco Electronics, asse piece rate scale: 1-20 unit: each for every unit over 3 his gross…

A: As per the guideline, I am supposed to solve only first question from the given problems.(4)To…

Q: How many murders per 100,000 residents can be expected in a state with 1.8 thousand automatic…

A: X denotes the thousands of atomic weapons Y denotes the murders per 100,000 residents. The estimated…

Q: We have data on the lean body mass and resting metabolic rate for 12 women who are subjects in a…

A: Calculate Fitting a straight line - Curve fitting using Least square method X Y 49.4 1070 45…

Q: Since the profit model is a cubic polynomial, the marginal profit is a linear polynomial, cubic…

A: Note: According to bartleby guidelines, solution of first three sub-parts will be provided.

Q: For the period 1970-1991 for the United States the following two rival consumption models were…

A: The model with the lowest AIC value being considered the ‘best’. From the provided information, the…

Q: Consider the following model of stock prices: Price=Bo + Biearning + ɛ. Where earning is the annual…

A: The sample size is the number of paired data values, that is n=10. Using the given data set and…

Q: ABC has opened a small printing shop 12 months ago. ABC give good printing services and the business…

A: The given data represents the overhead cost and its relationship with machine hours. Machine hours…

Q: Charles Lackey operates a bakery in Idaho Falls, Idaho. Because of its excellent product and…

A: Loaves produced (Output) loaves per monthLabor Cost (Work hours x Employee cost) Utility Cost per…

Q: Past sales for months 1 to 5 of a large equipment are shown below. Month 1 2 3 4 5 Actual Demands 12…

A: From the given information we forecast for 6 using least squared equation

Q: c) A week of performance data for another production line is given in Table Q6b. Assess and analyse…

A: We will use the basic knowledge of potential rates and performance analysis to answer this question…

Q: An online business sells two varieties of cat food, 'standard' and 'luxury'. It orders these from…

A: The cost of cat food increased by 9.6% between 2021 and 2022, which is less than the overall…

Q: Quiz 4 FC = Rs. 200,000 SP = Rs. 100 VC = Rs. 60 Total output = 8000 units. Calculate (1) BEP in…

A: Given, Total output= 8000 Fixed cost = 200,000 Selling price=100 variable cost=60…

Q: The process spread in a variable control chart is referred to as the process capability and is equal…

A: Given that The process spread in a variable control chart is referred to as the process capability…

Q: . Develop a linear-regression-based forecasting model to predict costs. b. Predict costs when…

A: Let X be the patient days Y be the Cost Given data, X Y X*Y X*X 516 32996 17025936 266256…

Q: What are stockout costs and capacity-associated costs? What is their relationship to inventories?

A: Stockout cost is the lost income and expense associated with a shortage of inventory .This cost can…

Q: Are the two estimated birth weights significantly different practically and statistically? Please…

A: To find the estimated or expected birth weights for a non-smoking woman A and a smoking woman B who…

Q: People with high blood pressure suffer from hypertension. Data on fasting blood sugar…

A: Given: Data on fasting blood sugar (milligrams/decilitre) and magnesium (milligrams/decilitre) in…

Q: 2. The table below presents data on annual labor income in a very simple, four-person economy, with…

A: A measure of income inequality that ranges from 0 (perfect equality: each income quintile has the…

Q: The net weight in pounds of a packaged chemical herbicide is uniform for 49.75 < x < 50.25 pounds.…

A: From the information, given thatLet X denotes the net weight of a packaged chemical herbicide in…

Question

100%

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: first we define the given data then solve step by step answer

VIEW

Step 2: now we will formulate a linear program to minimize the total dose to the entire healthy anatomy.

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A manufacturing firm produces its products in batches using sophisticated machines and equipment. The general manager wanted to investigate the relationship between direct labor costs and the number of units produced per batch. The recorded the data from the last 30 batches is below Batch Size Labor Cost Batch Size Labor Cost (5) 25 34 19 31 39 21 21 19 40 36 34 29 26 36 423 415 447 430 340 317 362 452 464 438 420 400 469 25 39. 25*8585& 29 31 21 36 39 29 41 35. 21 29 25 395 88888883 429 440 420 400 425 420 401 451 422 410 395 409 Determine the fixed and variable labor costs (Round your answers to the nearest cent) fixed cost 5 variable labor cost
The cost of goods sold for Veltron International last year amounted to $561,000, and the average inventory at cost was $374,000. The published inventory turnover at cost is 6.6. Calculate the inventory turnover at cost, and if it is less than the published rate, calculate the target average inventory at cost (in $). (If the actual turnover is greater than the published rate, enter "above" for target average inventory.) Inventory turnover at cost: Target average inventory at cost:
I need help with all the parts
(4
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…
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 54.9 43.9 39.4 43.5 36.6 44.5 47.9 46.4 53.8 54.3 43.9 51.5 Rate 990 1030 1220 1300 1460 1600 1450 1120 1280 1070 1070 1190 Find the least-squares regression line for predicting metabolic rate from body mass. ANSWER:
As a sales analyst for the shoe retailer Foot Locker, one of your responsibilities is measuring store productivity and then reporting your conclusion back to management. Foot Locker uses sales per square foot as a measure of store productivity. While preparing your report for the second quarter results (Q2), you are able to determine that annual sales for last year ran at a rate of $406 per square foot. Therefore, $406 per square foot will be your sales estimate for the population of all Foot Locker stores during Q2. For your Q2 Sales Report, you decide to take a random sample of 64 stores. Using annual data from last year, you are able to determine that the standard deviation for sales per square foot for all 3,400 stores was $80. Therefore $80 per square foot will be your population standard deviation when compiling your Q2 report. Management has asked for the probability that your sample mean based on 64 stores is 1) within $15 and 2) within $5 of the population mean…
2.) Consider an M/M/2 system with an arrival rate of 9 per minute and a service rate of 8 per minute. What is the average time a customer spends in the system? Take your answer to three decimal places. Omit the units in your answer.