Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Expert Solution & Answer
Chapter 3, Problem 26RP
Explanation of Solution
Constraint for the Linear
Constraint 1:
x1 | 0 | 3 |
x2 | 6 | 0 |
Constraint 2:
x1 | 0 | 4 |
x2 | 4 | 0 |
Constraint 3:
x1 | 0 | 10 |
x2 | 2 | 0 |
Graph for the above constraint:
The value of the objective function at each of these extreme points are as follows:
Extreme-coordinates | Lines-through-extremes |
Objective-function-value Z=5x1+x2 |
A(0, 6) |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Which of the following provide a solution for the following LP problem?
MAX: 3X1 +4X2
Subject to:
X1 ≤ 12
X2 ≤ 10
4X1 _ 6X2 ≤ 72
X1, X2 ≥ 0
X1 = 12, X2 = 3
X1= 18, X2=0
PROFIT = 54
PROFIT= 56
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?
The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem.
X2
X3
6
2
1
2
- 1
- 3
X1
1
3
-5
S₁
1
0
0
S2
0
1
0
Z
0
0
1
18
39
The maximum is | when x₁ = ₁X₂ = ₁ x3 =₁ $₁=₁ and $₂ = -
X3
(Type integers or simplified fractions.)
Chapter 3 Solutions
Introduction to mathematical programming
Ch. 3.1 - Prob. 1PCh. 3.1 - Prob. 2PCh. 3.1 - Prob. 3PCh. 3.1 - Prob. 4PCh. 3.1 - Prob. 5PCh. 3.2 - Prob. 1PCh. 3.2 - Prob. 2PCh. 3.2 - Prob. 3PCh. 3.2 - Prob. 4PCh. 3.2 - Prob. 5P
Ch. 3.2 - Prob. 6PCh. 3.3 - Prob. 1PCh. 3.3 - Prob. 2PCh. 3.3 - Prob. 3PCh. 3.3 - Prob. 4PCh. 3.3 - Prob. 5PCh. 3.3 - Prob. 6PCh. 3.3 - Prob. 7PCh. 3.3 - Prob. 8PCh. 3.3 - Prob. 9PCh. 3.3 - Prob. 10PCh. 3.4 - Prob. 1PCh. 3.4 - Prob. 2PCh. 3.4 - Prob. 3PCh. 3.4 - Prob. 4PCh. 3.5 - Prob. 1PCh. 3.5 - Prob. 2PCh. 3.5 - Prob. 3PCh. 3.5 - Prob. 4PCh. 3.5 - Prob. 5PCh. 3.5 - Prob. 6PCh. 3.5 - Prob. 7PCh. 3.6 - Prob. 1PCh. 3.6 - Prob. 2PCh. 3.6 - Prob. 3PCh. 3.6 - Prob. 4PCh. 3.6 - Prob. 5PCh. 3.7 - Prob. 1PCh. 3.8 - Prob. 1PCh. 3.8 - Prob. 2PCh. 3.8 - Prob. 3PCh. 3.8 - Prob. 4PCh. 3.8 - Prob. 5PCh. 3.8 - Prob. 6PCh. 3.8 - Prob. 7PCh. 3.8 - Prob. 8PCh. 3.8 - Prob. 9PCh. 3.8 - Prob. 10PCh. 3.8 - Prob. 11PCh. 3.8 - Prob. 12PCh. 3.8 - Prob. 13PCh. 3.8 - Prob. 14PCh. 3.9 - Prob. 1PCh. 3.9 - Prob. 2PCh. 3.9 - Prob. 3PCh. 3.9 - Prob. 4PCh. 3.9 - Prob. 5PCh. 3.9 - Prob. 6PCh. 3.9 - Prob. 7PCh. 3.9 - Prob. 8PCh. 3.9 - Prob. 9PCh. 3.9 - Prob. 10PCh. 3.9 - Prob. 11PCh. 3.9 - Prob. 12PCh. 3.9 - Prob. 13PCh. 3.9 - Prob. 14PCh. 3.10 - Prob. 1PCh. 3.10 - Prob. 2PCh. 3.10 - Prob. 3PCh. 3.10 - Prob. 4PCh. 3.10 - Prob. 5PCh. 3.10 - Prob. 6PCh. 3.10 - Prob. 7PCh. 3.10 - Prob. 8PCh. 3.10 - Prob. 9PCh. 3.11 - Prob. 1PCh. 3.11 - Show that Fincos objective function may also be...Ch. 3.11 - Prob. 3PCh. 3.11 - Prob. 4PCh. 3.11 - Prob. 7PCh. 3.11 - Prob. 8PCh. 3.11 - Prob. 9PCh. 3.12 - Prob. 2PCh. 3.12 - Prob. 3PCh. 3.12 - Prob. 4PCh. 3 - Prob. 1RPCh. 3 - Prob. 2RPCh. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - Prob. 8RPCh. 3 - Prob. 9RPCh. 3 - Prob. 10RPCh. 3 - Prob. 11RPCh. 3 - Prob. 12RPCh. 3 - Prob. 13RPCh. 3 - Prob. 14RPCh. 3 - Prob. 15RPCh. 3 - Prob. 16RPCh. 3 - Prob. 17RPCh. 3 - Prob. 18RPCh. 3 - Prob. 19RPCh. 3 - Prob. 20RPCh. 3 - Prob. 21RPCh. 3 - Prob. 22RPCh. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - Prob. 25RPCh. 3 - Prob. 26RPCh. 3 - Prob. 27RPCh. 3 - Prob. 28RPCh. 3 - Prob. 29RPCh. 3 - Prob. 30RPCh. 3 - Prob. 31RPCh. 3 - Prob. 32RPCh. 3 - Prob. 33RPCh. 3 - Prob. 34RPCh. 3 - Prob. 35RPCh. 3 - Prob. 36RPCh. 3 - Prob. 37RPCh. 3 - Prob. 38RPCh. 3 - Prob. 39RPCh. 3 - Prob. 40RPCh. 3 - Prob. 41RPCh. 3 - Prob. 42RPCh. 3 - Prob. 43RPCh. 3 - Prob. 44RPCh. 3 - Prob. 45RPCh. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Prob. 48RPCh. 3 - Prob. 49RPCh. 3 - Prob. 50RPCh. 3 - Prob. 51RPCh. 3 - Prob. 52RPCh. 3 - Prob. 53RPCh. 3 - Prob. 54RPCh. 3 - Prob. 56RPCh. 3 - Prob. 57RPCh. 3 - Prob. 58RPCh. 3 - Prob. 59RPCh. 3 - Prob. 60RPCh. 3 - Prob. 61RPCh. 3 - Prob. 62RPCh. 3 - Prob. 63RP
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
- 3 2: Solve the following linear program using the simplex method. Maximize z = 5x₁ + 4x₂ subject to 6x₁ + 4x₂ ≤ 24 X₁ + 2x₂ ≤6 -X₁ + X₂ ≤1 X₂ ≤2 X₁, X₂ ≥ 0arrow_forwardThe following table belongs to the optimal solition nit of a Lineer Programming Problem. Obtain the formulation of the initial problem. XI x2 ke -Jig 38 X₁ Xu O 1 O 19 41 14 23 38 xu O O 1 VI 38 A 38 AL A2 (1-38M) (2-19M) 38 19 -3 38 5 L 응급 31 19 19 solution 7' 2 5arrow_forwardusing Python/PuLP solve Turkeyco produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet consists of white meat and dark meat. Cutlet 1 sells for $4/lb and must consist of at least 70% white meat. Cutlet 2 sells for $3/lb and must consist of at least 60% white meat. At most, 50 lb of cutlet 1 and 30 lb of cutlet 2 can be sold. The two types of turkey used to manufacture the cutlets are purchased from the GobbleGobble Turkey Farm. Each type 1 turkey costs $10 and yields 5 lb of white meat and 2 lb of dark meat. Each type 2 turkey costs $8 and yields 3 lb of white meat and 3 lb of dark meat. Part A: Formulate an LP to maximize Turkeyco’s profit. Part B: Solve the LP (provide exact values for all variables and the optimal objective function).arrow_forward
- please solve in a quarter of an hour and they came An electricity distribution company wants to calculate the electricity fee to be paid by the subscriber according to the type of electricity usage place (Residential: u or U, Workplace: p or P) as follows; In workplaces; 3.78TL for each kilowatt-hour (kwh), In residences Up to the first 60 kWh, each kWh is 2.98 TL, Then, up to 120 kWh, each kWh is 3.62 TL, For more (more than 100 kWh), it charges 2.56 TL for each kWh. Using the C programming language, write an electricity bill calculation program in accordance with the rules below. 1-Use the switch.case structure while writing the program. 2-First, we ask the user for the 6-digit subscriber number. The user will enter a random 6-digit number after the program runs. 3- After entering the usage type, the first and last meter reading values will be entered randomly from the keyboard. Here, the first read value cannot be greater than the last read value. Create a blocking line for this…arrow_forwardEmployees of KB and SONS Consultants Limited are paid at an hourly basics of 25GHS per an hour for regular hours and 1.5 times per hour for overtime hours in a week. Any hour worked over 40 hours per week is overtime. The following national tax sliding scale is then applied to determine the amount of tax to be paid by an employee. GrossWage Tax Rate (%) First 125 0 Next 125 5 Next 1500 10 Next 2750 15 Next 1250 20 Excess over 5000 30 In addition 6% of an employee’s gross wage is withheld for Social Security, 3% is withheld as constituency tax and 20GHS is withheld by the employer as welfare contribution. If an employee has more than 3 dependants then an amount of 5GHS for each dependant in excess of three towards NHIS. You are required to write a program that compute a workers gross pay, the deductions and his/her net pay. Your program should allow details of the staff to be accept /input into the system for the necessary computations. Try using comments in explaining the flow of the…arrow_forwardThe 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 EXCELarrow_forward
- 7 Maximize z = 5x₁ + 4x₂ subject to 6x₁ + 4x₂ ≤ 24 X₁ + 2x₂ ≤6 -X₁ + X₂ ≤1 X₂ ≤2 X₁, X₂ ≥ 0 Solve the following linear program using the simplex method.arrow_forwardWhich of the following algorithms can be used to find the optimal solution of an ILP?(a) Enumeration method;(b) Branch and bound method;(c) Cutting plan method;(d) Approximation method.arrow_forward1. Use simple fixed-point iteration to locate the root of f(x) = sin (√) - x Use an initial guess of xo = 0.5 and iterate until & ≤ 0.01%.arrow_forward
- The table below describes the average voltage generated, A, in volts by an energy harvester for three days at three different times for each day. Referenced time Day 3. 3.0 V 1.8 V 0.9 V 1.9 V 2.2 V 1.7 V 0.5 V 1.1 V 2.2 V Given that the power generated in millivwatts (mW), P, can be calculated using the following equation: 500A? P = Where A is the voltage generated and R is the total resistance given as 2000 Q. Write a MATLAB/OCTAVE script to store the voltage data from the table as a single matrix, where the days represent the rows and the referenced times represent the columns of the matrix. Hence, in the same script, Calculate the power generated at each day and referenced time. i) ii) Compute and output the overall maximum power generated. Finally, compute and output the days and referenced times where the power generated exceeds 1.0 mW (Tips: You may want to use a nested loop OR the in-built MATLAB/OCTAVE function called 'find' here) iii)arrow_forwardQ1: For these Value Obtain U and V and evaluate W when Z = V5 – 2i Q2: If Z1= 4i-3 Z2= 3i Z1+Z2 Find Z2 (2x² x 2 2 Q3: if f(x) = 4 x < 2 find f(x)dx Q4: Show that f (z) = 2z3 – 4z + 1 is satisfy Cauch-Rieman %3D if Z in Cartesian formarrow_forwardWhich option is correct for the following system equation? x-y-z=4 2x-2y-2z=8 5x - 5y - 5z = 20 answer a)Finite solutions b)No solution c)Subzero solutions d)Infinitely many solutions e)Unique solutionarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
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