6 This problem shows why a dual variable y, corresponding to a z constraint in a max problem must satisfy y, < 0. a Using the rules given in the text, find the dual of max z = 3x, + x, X, + x2 s 1 s.t. X1, X2 2 0 b Transform the LP of part (a) into a normal max problem. Now use (16) and (17) to find the dual of the transformed LP. Let y, be the dual variable correspond- ing to the second primal constraint. c Show that, defining ỹ, = -y2, the dual in part (a) is equivalent to the dual in part (b).
Q: Consider the following problem: Minimize Z = 5X1 + 8X2 + 3X3 + 5X4 + 12X5…
A: Linear Programming Problem or LPP can be defined as the mathematical technique that is used to…
Q: Find the optimum solution for the following Integer Linear Programming problem using the Cutting…
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Solve for the linear programming 1. Minimize Z=3x+5y so that x+3y >=3…
A: The first question is solved below. Kindly post the second question separately.
Q: b) Consider the following LP problem: Maximize z = 5x, + 2x2 Subject to 4x, - 2x2 < 40 X1 + 2x2 25…
A: Given: Max Z = 5 x1 + 2x2 subject to4 x1 - 2 x2 ≤ 40x1 + 2 x2 ≥ 5and x1,x2≥0;
Q: 6. A firm produces four products: A, B, C. and D. Each unit of product A requires two hours of…
A: Objective Functions and Constraints: Based on the given details, the objective…
Q: 8.1. Consider the problem minimize f(x) = e* subject to x > 1. What is the solution to this problem?…
A: The detailed solution to this question is given in Step 2.
Q: 11. The shadow price is calculated to be 5 for a less than or equal to constraint in a maximization…
A: Note:As per bartleyby guidelines i have answered first multiple choice question..pls post remainind…
Q: Consider the following linear programming problem: Min Z = 6x1 + 4x2 Subject to: 4x1 + 2x2 2 100 2x1…
A: Given LP- Min Z = 6X1+4X2 Subject to Constraints- 4X1+2X2≥100 2X1+3X2≥90X1, X2≥0
Q: Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What…
A:
Q: 4-3) The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef…
A: Let A and B be the quantities of ingredients A and B respectively. Objective function: Min Z=50A…
Q: (a) Is it necessary that the feasible region for a maximisation type of linear programming problem…
A: Feasible sets might be bounded or unbounded. For instance, if the feasible set is being defined by…
Q: 6. The Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to three…
A: Given: Total number of salespeople = 12 Profit earned per month by a salesperson in south = $600…
Q: Consider the following linear programming formulation: Min 5x + 2y Subject to (1)…
A: Note: Since you have posted multiple independent questions in the same request, we will solve the…
Q: 2.3.5. Mixed Constraints Linear Programming Problem Example 14: Use the graphical method to solve…
A: Linear programming is a mathematical technique that is also used in operations management…
Q: The optimal solution of this linear programming problem is at the intersection of constraints 1 (c)…
A: Objective function: Max 2X1 + X2 Constraint: s.t. 4X1 + 1X2 ≤ 400 4X1 + 3X2 ≤ 600…
Q: The number of crimes in each of a city’s three policeprecincts depends on the number of patrol cars…
A:
Q: 9 Graphically determine two optimal solutions to the following LP: min z = 3x, + 5x2 3x, + 2x2 2 36…
A: Optimal Solution refers to the feasible solution for satisfying the set of constraints. The…
Q: 28 and 35 are two feasible solutions to a primal minimization problem. Which statement is the most…
A: Linear programming can be stated as the technique of amending or optimizing operations with…
Q: Find the complete optimal solution to this linear programming problem. ObjectiveFunction : Minimize…
A:
Q: 1- An enterprise aiming to produce low and high quality varnishes plans to produce by mixing 121…
A: Given data is Limit for alcohol = 121 barrels Limit for resin = 49 barrels Alcohol in low-quality…
Q: Minimize: Z = 4x1 + 2x2 + x3 Subject to: 2x1 + 3x2 + 4x3 ≤ 14 3x1 + x2 + 5x3 ≥ 4 x1 + 4x2 + 3x3 ≥…
A: The purpose of Linear Programming Problems (LPP) is to find the optimal value for a given linear…
Q: max z = 3x + 2x2 12 s1 82 rhs 2x1 + 5x2 < 8 3x1 + 7x2 < 10 *1, 12 2 1 0 0 0 1/3 1 -2/3 4/3 0 1 7/3 0…
A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…
Q: 3. Consider the following all-integer linear program: Max 1x₁ + 1x₂ s.t. 4x1 + 6x2 22 1x₁ + 5x₂ = 15…
A: Given LP- Maximize Z= 1x1+1x2Subject to -4x1+6x2≤ 22 1x1+5x2≤15 2x1+1x2≤9 x1, x2≥0 and integer…
Q: 2(a) The tableau is not optimal for either maximization or a minimization problem. Thus, when a…
A: The given tableau - Basic x1 x2 x3 x4 x5 x6 x7 x8 Solution Z 0 -5 0 4 -1 -10 0 0 620 x8 0 3 0…
Q: Šolve the following linear Programming Problem Minimize W = 11x, + 2x2 + 4xX3 Subject to 4x1 + x2 +…
A: MIN Z = 11x1 + 2x2 + 4x3......................................(hence, W=Z)subject to4x1 + x2 + x3…
Q: x1 + x2 ≤30 300 ≤5x1 + 6x2 x1 ≥0, x2 ≥0. From the given constraint above, provide the following a.…
A: Linear programming is a mathematical technique that is also used in operations management…
Q: 1. Given the following linear programming model: Minimize Z = 480x1 + 160x2 subject to…
A: Please note that as you have posted more than one question, the first question with two subparts is…
Q: Q3:A/ Find the solution to the following linear programming problem by dual simplex method Min Z=…
A: It's important to remember that perhaps the conventional (primal) simplex approach is a method that…
Q: 4. Solve the problem given with the constrains and objective function. Maximize profit 30X1 + 40X2…
A: Objective Functions and Constraints: Based on the given details, the objective…
Q: 21. Ye Olde Cording Winery in Peoria, Illinois, makes three kinds of authentic German wine:…
A: This question is related to the topic of Decision Making and this topic falls under the operations…
Q: For the following set of equation an initial BF solution can be 5 x, + 2 x2 +3 x3 + X4 = 9 X1 + 4 x2…
A: Given data: The set of equations 5X1 + 2X2 + 3X3 +X4 = 9 X1 + 4X2 + 2X3 +X5 = 8 2X1 +X3 +X6 = 11…
Q: 2(a) The tableau is not optimal for either maximization or a minimization problem. Thus, when a…
A: The given tableau- Basic X1 X2 X3 X4 X5 X6 X7 X8 Solution Z 0 -5 0 4 -1 -10 0 0 620 X8 0 3 0…
Q: 2. A power plant has three boilers. If a given boiler is operated, it can be used to produce a…
A:
Q: b) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a…
A: The objective of the maximal flow network diagram is to find the maximum output the firm can get…
Q: Convert into a maximization problem with positive constants on the right side of each constraint,…
A: The question is related to maximizatiin Problem of Linear Programming and the initial table of…
Q: 1. Given the following linear programming model: Minimize Z = 480x1 + 160x2 subject to…
A:
Q: 3. Consider the following linear program: Min 8X + 12Y s.t. IX + 3Y 9 2X+ 2Y 10 6X + 2Y 18 X, Y 0…
A: Note: - Since we can answer only up to three subparts we will answer the first three(a, b, and c)…
Q: The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats…
A: The given data can be represented tabularly as follow: Oats Rice Minimum requirement Vitamin…
Q: 3-38. Consider the following set of constraints: X1 + x2 + x3 = 7 2x1 - 5x2 + x3 > 10 X1, X2, X3 2 0…
A:
Q: 7. The following questions refer to a capital budgeting problem with six projects represented by 0-1…
A: Given: Here, Six projects are represented by 0-1 variables, X1= Project 1X2 = Project 2X3 =…
Q: FIGURE 3.14 THE SOLUTION FOR THE INVESTMENT ADVISORS PROBLEM Optimal Objective Value = 8400.00000…
A: Note: - Since we can answer only up to three subparts we will answer the first three subparts(a, b,…
Q: Carefully examine the following ASSIGNMENT problem. Which of the following constraints is not true?…
A: In assignment problem we assign one job to machine to get all the job done with a minimum cost…
Q: 5. Consider the following LP problem: Maximize z = 2x1 + 4x2 + 4x3 - 3x4 Subject to X1 + x2 + x3 = 4…
A: The linear programming process is a process through which the value of the variables that maximize…
Q: 1) The Texas Consolidated Electronics Company is contemplating a research and development (R&D)…
A: Given data is Project Expense Scientists required Profit 1 $60,000 7 $3,60,000 2 $1,10,000 9…
Q: a. The Objective Function b. All the constraints that the solution must satisfy, including…
A: The process through which the values of the variables that maximize or minimize a given linear…
Q: 4. Mathematical model and optimal simplex table of a LP problem are given below. Calculate lower and…
A: Find the Given details below: Based on the given details, the objective functions and constraints…
Q: Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2…
A: Please find the attached answer in the step 2
Q: (2). A company produces tables at its two factories A and B. The next three months, the company must…
A: Month Demand 1 300 2 400 3 500 The cost details: Labor hours Cost Factory A 1.5 hrs…
Q: Convert into a maximization problem with positive constants on the right side of each constraint,…
A:
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
- 4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.Indetify the constraints that form the fesible region and identify the constraints that are rebundant. Equation: Maximize 5x1 + 3x2 Subjected to x1 + 5x2 ≤ 5 4x1 + 3x2 ≤ 12 x1 + x2 ≤ 4 x1 + x2 ≤ 5 5x1 + 7x2 ≤ 35 x1 + x2 ≥ 0Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 6R + 9C s.t. R + 3 2 C ≤ 1,000 Cutting and sewing 1 2 R + 1 3 C ≤ 300 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHSValue AllowableIncrease AllowableDecrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3…
- Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2 C ≤ 800 Cutting and sewing 1 2 R + 1 3 C ≤ 240 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3520.00000 Variable Value Reduced Cost R 320.00000 0.00000 C 240.00000 0.00000 Constraint Slack/Surplus Dual Value 1 120.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHSValue AllowableIncrease AllowableDecrease 1 800.00000 Infinite 120.00000 2 240.00000 160.00000 106.66667 3…Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2 C ≤ 800 Cutting and sewing 1 2 R + 1 3 C ≤ 280 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3640.00000 Variable Value Reduced Cost R 440.00000 0.00000 C 180.00000 0.00000 Constraint Slack/Surplus Dual Value 1 90.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHSValue AllowableIncrease AllowableDecrease 1 800.00000 Infinite 90.00000 2 280.00000 120.00000 146.66667 3 100.00000 18.00000 30.00000 (a) Determine the objective coefficient ranges. (Round your answers to two decimal places.)…b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?
- Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 04 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.
- Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 2? a. Entering Variable: x and Leaving Variable: S2 b. Entering Variable: y and Leaving Variable: S2 c. Entering Variable: y and Leaving Variable: S1 d. Entering Variable: x and Leaving Variable: S111. The shadow price is calculated to be 5 for a less than or equal to constraint in a maximization LP problem, this means: a. if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 5 b. if the RHS for that constraint is increased by one then the optimal objective function value is increase by 5 c. if the RHS for that constraint is increased by 5 then the optimal objective function value is increase by 1 d. if the coefficient of the objective function is increase by 5 then the RHS for that constraint must be increased by 1 12. Sensitivity Analysis generally assumes a. we are considering a change in two input data values at a time b. are considering a change in only one input data value at a time c. we are considering several change in several input data…Consider the following LP model in standard form, with a row for the objective function Z. a) Put it into Canonical form ( or Simplex Tableau form) with basic variables X1, X2 , and X3. b) Determine the association BFS (Basic Feasible Solution) and the new formula for the objective function Z Minimize 10X1 + 4X2 Sujbject to 3X1 + 2X2 - X3 = 60 7X1 + 2X2 - X4 = 84 3X1 + 6X2 -X5 = 72 X1, X2, X3 , X4 , X5 >= 0