Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 6.8, Problem 9P
Program Plan Intro
100% Rule for changing objective function coefficient:
In 100% Rule, there are two cases has to be considered depending on whether the objective function coefficient of any variable with a zero reduced cost in the optimal tableau is changed.
Case 1: All the variables whose objective function coefficients are changed have non-zero reduced cost in the optimal row 0.
Case 2: At least one variable whose objective function coefficient is changed has a reduced cost of zero.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The Pee Tool Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings
for electronic consumer products. All four presses operate differently and are of different sizes.
Currently the firm has a contract to produce three products. The contract calls for 400 units of product
1; 570 units of product 2; and 320 units of product 3. The time (in minutes) required for each product
to be produced on each machine is as follows: SOLVE THE MODEL BY USING MS EXCEL
Using Python/PuLP solve
At the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit.
Table 2
Month
Revenues ($)
Bills ($)
1
400
600
2
800
500
3
300
500
4
300
250
Excercise 3.1
A book salesperson living in New York needs to visit clients in Utah, Jersey, LA, and Milan within a month. The distances between these cities are given in the table in the picture.
Find the optimal solution to the problem using the branch-and-bound method.
Please detailed :( Thank you so much
Chapter 6 Solutions
Operations Research : Applications and Algorithms
Ch. 6.1 - Prob. 1PCh. 6.1 - Prob. 2PCh. 6.1 - Prob. 3PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.3 - Prob. 3P
Ch. 6.3 - Prob. 4PCh. 6.3 - Prob. 5PCh. 6.3 - Prob. 6PCh. 6.3 - Prob. 7PCh. 6.3 - Prob. 8PCh. 6.3 - Prob. 9PCh. 6.4 - Prob. 1PCh. 6.4 - Prob. 2PCh. 6.4 - Prob. 3PCh. 6.4 - Prob. 4PCh. 6.4 - Prob. 5PCh. 6.4 - Prob. 6PCh. 6.4 - Prob. 7PCh. 6.4 - Prob. 8PCh. 6.4 - Prob. 9PCh. 6.4 - Prob. 10PCh. 6.4 - Prob. 11PCh. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.5 - Prob. 1PCh. 6.5 -
Find the duals of the following LPs:
Ch. 6.5 - Prob. 3PCh. 6.5 - Prob. 4PCh. 6.5 - Prob. 5PCh. 6.5 - Prob. 6PCh. 6.6 - Prob. 1PCh. 6.6 - Prob. 2PCh. 6.7 - Prob. 1PCh. 6.7 - Prob. 2PCh. 6.7 - Prob. 3PCh. 6.7 - Prob. 4PCh. 6.7 - Prob. 5PCh. 6.7 - Prob. 6PCh. 6.7 - Prob. 7PCh. 6.7 - Prob. 8PCh. 6.7 - Prob. 9PCh. 6.8 - Prob. 1PCh. 6.8 - Prob. 2PCh. 6.8 - Prob. 3PCh. 6.8 - Prob. 4PCh. 6.8 - Prob. 5PCh. 6.8 - Prob. 6PCh. 6.8 - Prob. 8PCh. 6.8 - Prob. 9PCh. 6.8 - Prob. 10PCh. 6.8 - Prob. 11PCh. 6.9 - Prob. 1PCh. 6.9 - Prob. 2PCh. 6.9 - Prob. 3PCh. 6.10 - Prob. 1PCh. 6.10 - Prob. 2PCh. 6.10 - Prob. 3PCh. 6.11 - Prob. 1PCh. 6.11 - Prob. 3PCh. 6.11 - Prob. 4PCh. 6.12 - Prob. 5PCh. 6.12 - Prob. 6PCh. 6.12 - Prob. 7PCh. 6 - Prob. 1RPCh. 6 - Prob. 2RPCh. 6 - Prob. 3RPCh. 6 - Prob. 4RPCh. 6 - Prob. 5RPCh. 6 - Prob. 6RPCh. 6 - Prob. 7RPCh. 6 - Prob. 8RPCh. 6 - Prob. 9RPCh. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 13RPCh. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 17RPCh. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - Prob. 25RPCh. 6 - Prob. 29RPCh. 6 - Prob. 33RPCh. 6 - Prob. 34RPCh. 6 - Prob. 35RPCh. 6 - Prob. 36RPCh. 6 - Prob. 37RP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below. Bulldozer/ A B C D Site Students 1 90 75 75 80 solve it 2 35 85 55 65 yourself 3 125 95 90 105 4 45 110 95 115 How should the bulldozers be moved to the construction sites in order to minimize the total distance traveled?arrow_forwardb) Consider the following linear programming problem: Min z = x1 + x2 s.t. 3x1 – 2x2 < 5 X1 + x2 < 3 3x1 + 3x2 2 9 X1, X2 2 0 Using the graphical approach, determine the possible optimal solution(s) and comment on the special case involved, if any.arrow_forwardQuestion 2At the peak of COVID-19, most worker started working from home. Salaries of workers were reduced by 30%. Assuming income tax was also reduced by 50% from the previous rate of 15% and workers were paid on the number of hour worked in a month and each worker is supposed to work a total of 170 hours in a month. All overtime has been cancelled. If a worker does not meet the 170 hours’ threshold for a month, 5% is deducted from the salary. Assuming the hourly rate is GHC 10, Write a java program for the scenario narrated above. Your program should:a) request for an employee’s name, the number of hours worked in a month b) define a method called payRole, your method should compute a worker’s salary and income tax and any deductions if any.c) your program should display the results in “b” above. d) explain the logic behind the code especially the methodarrow_forward
- At the peak of COVID-19, most worker started working from home. Salaries of workers were reduced by 30%. Assuming income tax was also reduced by 50% from the previous rate of 15% and workers were paid on the number of hour worked in a month and each worker is supposed to work a total of 170 hours in a month. All overtime has been cancelled. If a worker does not meet the 170 hours’ threshold for a month, 5% is deducted from the salary. Write a c++ program for the scenario narrated above. Your program should: a) request for an employee’s name, the number of hours worked in a month b) define a function called payRole, your function should compute a worker’s salary and income tax and any deductions if any c) your program should display the results in “b” above. d) explain the logic behind the code especially the functionarrow_forward1. Consider an instance of the Knapsack Problem without repetitions with 4 items, having weights and values as follows. The weights (in pounds) are w1=2, w2 =7, w3 =10, w4 =12. The dollar values of these items are respectively v1 = 12, v2 = 28, v3 = 30, v4 = 5. The capacity of the knapsack is 12. (a) Find the optimal solution for Fractional Knapsack. (b) Find the optimal solution for 0-1 Knapsack.arrow_forwardAt the peak of COVID-19, most worker started working from home. Salaries of workers were reduced by 30%. Assuming income tax was also reduced by 50% from the previous rate of 15% and workers were paid on the number of hour worked in a month and each worker is supposed to work a total of 170 hours in a month. All overtime has been cancelled. If a worker does not meet the 170 hours’ threshold for a month, 5% is deducted from the salary. Assuming the hourly rate is GHC 10, Write a java program for the scenario narrated above. Your program should:a) request for an employee’s name, the number of hours worked in a month b) define a method called payRole, your method should compute a worker’s salary and income tax and any deductions if anyc) your program should display the results in “b” above. d) explain the logic behind the code especially the methodarrow_forward
- 2 The Optimal Order paper company has received orders for four different groups of publications. The following orders have been placed. 8 rolls of 2 ft. paper at $2.50 per roll 6 rolls of 2.5 ft. paper at $3.10 per roll 5 rolls of 4 ft. paper at $5.25 per roll 4 rolls of 3 ft. paper at $4.40 per roll Due to heavy demand on the printing process, the paper company only has 13 ft. of paper from which to fill these orders. If partial orders (1 roll,2 rolls,3 rolls, etc.) can be filled, which orders and how many of each should be filled to maximize total profit? Use Dynamic Programming to answer the question and show stages 4 and 3 only.arrow_forwardVariable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease Туре А 4 -3.5 1E+30 Туре B y Туре С 3. 6. 2 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease Hours 1. 15 1 15 12 8. Plastic 20 30 1E+30 30 Cotton 70 70 40 55 Calculate the optimal value of the objective function if the coefficient of "x" changes to 4 and the coefficient of "y" changes to 3.5. Hint: Since it is proposing a simultaneous change (more than one change at a time), we have to check the 100% rule. **Enter the number only** **Do not use any words or symbols** Answer: 5 M 5arrow_forwardIn regards of the problem:max cTx subject to Ax = b, with an optimal solution of value v. Suppose the problem min cT x, subject to Ax = b have great with the same value, v. It can be concluded that there is a singlegood point for both? How is the feasible region geometrically?arrow_forward
- At the peak of COVID-19, most worker started working from home. Salaries ofworkers were reduced by 30%. Assuming income tax was also reduced by 50%from the previous rate of 15% and workers were paid on the number of hoursworked in a month and each worker is supposed to work a total of 170 hours ina month. All overtime has been cancelled. If a worker does not meet the 170hours’ threshold for a month, 5% is deducted from the salary. Assuming thehourly rate is GHC 10, Write a c++ program for the scenario narrated above.Your program should:a) request for an employee’s name, the number of hours worked in amonthb) define a function called payRole, your function should compute aworker’s salary and income tax and any deductions if any c) your program should display the results in “b” above. d) explain the logic behind the code especially the functionarrow_forward6. Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts. Provide a dynamic programming approach to solve this problem given an initial rod of length n with potential cut lengths of 1, 2, 5, and 7 [Adapted from ITA, pg. 370, 15.1-3] length of cut (i) 1 2 5 7 value (pi) 5 7 30 45 handling cost (ci) 4.5 6 10.5 13.5arrow_forwardConsider the following linear programming problem: Min A + 2B s.t. A + 4B ≤ 21 2A + B ≥ 7 3A + 1.5B ≤ 21 -2A + 6B ≥ 0 A, B ≥ 0 Determine the amount of slack or surplus for each constraint. If required, round your answers to one decimal place. (1) A + 4B ≤ 21 Slack or surplus (2) 2A + B ≥ 7 Slack or surplus (3) 3A + 1.5B ≤ 21 Slack or surplus (4) -2A + 6B ≥ 0 Slack or surplusarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole