Answered: Find solution using simplex method. MAX…

Find solution using simplex method. MAX Z = 6x1 + 4x2 subject to 2x1 + 3x2 ≤ 30 3x1 + 2x2 ≤ 24 x1 + x2 ≥ 3 and x1,x2 ≥ 0

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 73P

See similar textbooks

Related questions

Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…

Q: . Solve the following linear programming model graphically: minimize Z = 3x, + 6x2 kubject to 3x +…

A: A way of optimizing operations with some constraints is linear programming. Linear programming's…

Q: The constraint 5x 1 − 2x 2 ≤ 0 passes through the point (20, 50). True False

A: The answer is True.

Q: *Find the solution to the following linear programming problem by dual simplex method Min Z= 2X₁+4X,…

Q: Find solution using simplex method MAX Z = 6x1 + 4x2 subject to x1 + x2 ≤ 5 x2 ≥ 8 and x1,x2 ≥ 0

A: The problem is converted to canonical form by adding slack, surplus, and artificial variables as…

Q: Consider the following problem. Max Z-x₁ + 4x₂ Subject to: - 3x₁ + x₂ ≤ 6 x₁ + 2x₂ ≤ 4 X₂ ≥-3 X₁…

A: Simplex algorithm is a method in linear programming, which is used to calculate the optimal…

Q: Use the Simplex algorithm to solve the following LP models: а. max z = 2xi – x2 + x3 3x1 + x2 + X3 <…

A: Note: Since you have posted multiple independent questions in the same request, we will solve the…

Q: What is the special case that is associated with the following Linear ?Programming problem Max Z=…

A: Linear programming is nothing but the simple approach where an individual can represent complex…

Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…

A: The initial tableau can be written as follows.

Q: Set up and solve the following simple linear optimization model: MAX: 23.0 x + 16.9 y subject to: 3x…

A: Given that - MAX: 23.0x + 16.9y Subject to 3x + 4y ≥ 20 4x ≥ 10 5x + 1y ≤ 71 xy ≥ 0

Q: What special case in linear programming does the following graph depict? 10 X2 8 2 0 2x₁+x₂57 2 A)…

A: Ans) This graph has two constraints. 1 Constraint is less than type and other is greater than type.…

Q: subject to X - 2x, + x, 2 20 2x, + 4.x2 + X3 = 50 and X, 2 0, X2 2 0, X3 2 0. (a) Using the Big M…

A: according to u answering A given,

Q: Solve this using Simplex method Maximize: 4x1 + 2x2 + 5x3 S.t. x1 + 2x2 + x3 =0

A: The problem is converted to canonical form by adding slack, surplus, and artificial variables as…

Q: Graph the feasible region for the system of inequalities. 5x+y 3

A: A feasible region is an area illustrated by a set of coordinates that fulfill a system of…

Q: a) Use the Simplex Method with Artificial constraints to determine the optimal solution to the…

Q: (b) Use the simplex method to solve the following LP problem. Maximize, Z = 3x1 +4x2 Subject to 2x1…

A: A small introduction about the simplex method: The simplex approach uses slack variables,…

Q: Solve the following problem with Excel Solver:Maximize Z = 3X + Y.1 2X + 14Y ≤ 85 3 X + 2Y ≤ 18Y≤ 4

A: Formula:

Q: Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 6x1 + 5x2 ≤ 28…

A: SOLVING IN EXCEL SOLVER INFORMATION FOR CELL FORMULAS : CONSTRAINTS : CELL I11 =…

Q: Find the complete optimal solution to this linear programming problem. ObjectiveFunction : Minimize…

Q: Find the optimal solution of the following LP models. Maximize z= 15x1+20x2 Subject to: x1+2x2…

A: THE ANSWER IS AS BELOW:

Q: Suppose a linear program graph results in a number line for the binding constraints as follows: -3…

A: Give, Objective function- Max 5X1 + 10X2

Q: Write the Dual Problem for the below Primal prblem: Min. Z = 6X1 + 3X2 S. T. 6X1 + 3X2 + X3 >= 2 2X1…

A: The dual problem is converted from the primal problem using the following rules. 1. Minimization…

Q: Consider the following all-integer linear program: max 5x1 + 8x2 s.t. 9x1 + 4x2 ≤ 36 1x1 + 2x2 ≤ 10…

A: (a) The constraint 6x1 + 5x2 < 30 corresponds to the origin side of the line 6x1 + 5x2 = 30 The…

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: Solve using the simplex method the following problem: Maximize Z=3X1 + 2X2 subject to: 2X1+ X2 ≤ 18…

A: Problem is Max Z = 3 x1 + 2 x2 subject to 2 x1 + x2…

Q: Given this linear programming model, solve the model and then answer the questions that…

A: Formula:

Q: A company has 30,000 employees in three cities as shown in the table below. It wishes to give…

A: How to use Hamilton's Method Approach: First divide the total number of employees (30,000) with…

Q: Use the graphical method to solve the following problem: max Z = 2x1 + x2 subject to: 3x1 + x2 ≤…

A: The objective function of the linear programming problem as given in the question is, Subject to…

Q: 5 Use the simplex algorithm to find the optimal solution to the following LP: min z = -x1 - 2x2 s.t.…

A: Iteration 1: Zj-Cj = 2 Column index = 2 Entering variable= x2. Minimum ratio =3 Row index = 2…

Q: Use the graphical method to solve the following problem: max Z = 2x1 + x2 subject to: 6x1 + x2 ≤…

A: Below is the solution:-

Q: A linear programming problem is given as follows: maximize ? = 50x1 + 80x2 + 64x3 + 80x4…

A: Here, we would maximize the objective value, Maximize the Objective function =50x1 + 80x2 + 64x3 +…

Q: Graph the feasible region for the system of inequalities. 4x+y≤3 x-y>3

A: A feasible region is an area illustrated by a set of coordinates that fulfill a system of…

Q: Find the maximum and minimum values of the objective function p = 5x – 6y under the constraints y –…

Q: · Solve the following problem by the simplex method: Мах 12х, + 18х + 10хз 2x, + 3x2 + 4x3 0 X1,…

A: Problem is Max Z = 12 x1 + 18 x2 + 10 x3 subject to 2 x1 + 3 x2 + 4 x3 ≤ 50…

Q: Use the simplex algorithm to solve the following LP: max z x1 x2 x3 s.t. x1 2x2 2x3 20

A: Given LP Equation- LP: max z=x1+ x2 + x3

Q: min z = 3x1 2x1 + x2 2 6 3x1 + 2x2 = 4 s.t. X1, X2 2 0

Q: subject to X1 – 2x, + x, 2 20 2x, + 4x2 + X3 = 50 and X, 2 0, X2 2 0, X3 2 0. (a) Using the Big M…

A: Objective Functions and Constraints: Based on the given details, the objective…

Q: Compute the objective function value for the following problem: Min 260X + 65Y subject to : 2X>=0…

Q: Use the simplex method to solve the linear programming problem. Maximize z = 900x, + 500x2 + 300x3…

A: Max Z = 900 x1 + 500 x2 + 300 x3 subject to x1 + x2 + x3 ≤ 130 2 x1 + 3 x2…

Q: Use the simplex method to find the optimal solutions of the following LP Problem. Max. Z = 7x1 + 5x2…

A: Linear programming is a mathematical technique that is also used in operations management…

Q: Use the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 <…

A: Given Information: Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 +…

Q: Find the values of x1 and x2 where the following two constraints intersect. (Negative values should…

A: The detailed solution of the given question is in Step 2

Q: max TR = 8x, + 10x2 subject to 0.5x; s0 8x s 32 Sx: 2 10 X 20 6-1,2) -X + 4x, + Calculate the primal…

Q: Consider the following linear program: Maximize 30X1 + 10X, Subject to: 3X +X, < 300 X +X, s200 X1s…

Q: Find the solution using two-phase met hod Minimize Z = r+2x2 + 3x3-4 Subject to the constraints 5r,…

A: This question is related to the topic Decision Making and this topic falls under the business…

Q: In minimization problem we reashed optimal solution when all value in Cj-Zj row less than or equal…

A: The minimization problem is a linear programming (LP) problem. It can be solved efficiently using…

Q: Solve the following linear program using the full tableau implementation of the Simplex Method. max…

A: Here, The LP formulation is given below: Max Z=60*X1+30*X2+20*X3 Constraints are stated below:…

Q: Minimize Z = -5x1 + 4r2 subject to 213 x2 + 4r3 < 3 2x2 + 6x3 < 10 (1) (2) I1 2 0, x2 2 0, x3 2 0.…

A: GivenMIN Z = -5x1 + 4x2 - 2x3subject tox1 - x2 + 4x3 <= 33x1 - 2x2 + 6x3 <= 10and x1,x2,x3…

Concept explainers

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

100%

Find solution using simplex method.
MAX Z = 6x1 + 4x2
subject to
2x1 + 3x2 ≤ 30
3x1 + 2x2 ≤ 24
x1 + x2 ≥ 3
and x1,x2 ≥ 0

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.

Similar questions

Use the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =
Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.
Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .
Solve by the Big M – method: Maximize Ζ= x1 + 2x2 −3x3 + x4 Subject to x1 +2x2 +3x3 =15 2x1 +x2 + 5x3 = 20 x1 +2x2 +x3 +x4 = 10 x1 + 4x2 +6x3 ≤ 5 Where x x x x1, 2, 3, 4 ≥ 0
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 ≥ 0
Solve using the simplex method (Use Excel Solver) Maximize P = 6 x1 + 3x2 subject to -2 x + 3x <= 9 -x1 + 3x2 <= 12 x1, x2 >=0
Find the optimal solution of the following LP models. Maximize z= 15x1+20x2 Subject to: x1+2x2 ≥ 10 2x1 - 3x2 ≤ 6 x1+x2 ≥ 6 x1,x2 ≥ 0
Max Z = 6X1 + 18X2+20X3 Sub to X1 + X2 +X3 = 60 10X1 +15X2 +20X3 = 900 2X1 + 3X2 +3X3≤100 And X1, X2, X3 >=0 (SOLVE MANUALLY USING SIMPLEX METHOD PLEASE DON'T USE SHORTCUTS)
Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 12
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?
Given the following LP: Min 4x1 + 6x2 s.t 2x1 + 2x2 ≥ 3, x1 + 3x2 ≥ 2, x1 + 3x2 ≥ 0, Find its dual LP. Use graphical method or the Simplex algorithm, solve the primal LP in (1). Use graphical method or the Simplex algorithm, solve the dual LP (that you find in Part A). Find its dual LP.
Consider the following all-integer linear program:max 5x1 + 8x2s.t. 9x1 + 4x2 ≤ 361x1 + 2x2 ≤ 10x1, x2 ≥ 0 and integer.