Solve the following problem after finding its dual. Min z = x1 - 3x2 + 3x3 s.t. 3x1 - x2 + 2 x3 ≤ 7 2x1 + 4x2 ≥ -12 -4x1 + 3x2 + 8x3 ≤ 10 x1, x2, x3 ≥ 0
Q: Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7y…
A: Given- LP problem - Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0
Q: Explain what is meant by the feasible region and feasible solution of a graphical linear programming…
A: It is a linear optimization approach used to find the optimum solution to the problem at hand. A…
Q: Below tables show the Answer Report and the Sensitivity Report of the optimization Based on these…
A: a) Objective function is: Max 12X1+8X2+10X3+6X4…
Q: Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 4y − 6z =…
A: The step by step solution of the same is as follows:
Q: Consider the following set of constraints (Maixmization problem): 43X+ 86Y>= 29, and 129X+ 43Y >=…
A: Maximization fundamentally indicates trying to maximize/minimize the value of this linear function,…
Q: Minimize Z = -4x1 + x2 Subject to 8x1 + 2x2 =>16 4x1 + 2x2 =0 Identify the feasible solution area…
A:
Q: Doug Turner Food Processors wishes to introduce a new brand of dog biscuits composed of chicken- and…
A: Objective Functions and Constraints: Based on the given details, we found the…
Q: Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a…
A:
Q: What is true about the assignment problem if the solution has reached the table below? Project A…
A: a. The minimum number of vertical and horizontal lines needed to cross out 0s is not three, its…
Q: . Solve the following linear program graphically: Maximize P = - 4X1 + 3X2 Subject to 6X1 + 3X2 10…
A: *** I have answered the first question as it includes total three question, according to guideline,…
Q: To formulate a minimization problem for solution by the simplex method, we must add slack variables…
A: The slack variable is a variable that is added to an inequality constraint to transform it into an…
Q: For the linear program Max 2A + 3B s.t. 1A + 2B = 0 find the optimal solution…
A:
Q: What is Optimization? How many methods are there to calculate it? Explain this?
A: Hello thank you for the question. As per guidelines, we would provide only one answer at a time.…
Q: Enumerate and explain the problems of the BigBang theory and what theory answers or gives a solution…
A: Solution Big-Bang theory at a Glance - The big bang theory tries to explain how the world grew from…
Q: the optimal solution for the following problem. (Round your answers to 3 decimal places.)…
A: MAX Z = 8x1 + 8x2subject to7x1 + 9x2 >= 1610x1 + 10x2 >= 22and x1,x2 >= 0
Q: With reference to the solution of LPP simplex method table when do you Conclude as follows : LPP has…
A: The linear programming method is a mathematical algorithm method that aims at either of the two…
Q: Consider the following linear programming problem: Max 3A + 3B s.t 2A + 4B 0 a. Find the…
A: The question is related to Linear Programming. The question is of Maximization.
Q: Consider the following puzzle. You are to pick out 4three-letter “words” from the following list:DBA…
A: Conditions:- • The sum of the positions in the alphabet for the first letters of the four words…
Q: Job (Time in Minutes) 1 3 4 Worker A 5 5 7 B 8 4 4 5 5 8 4 7 4 5 5 2.
A: Assignment problem is used to minimize time, cost and maximize profit, productivity, etc. this is…
Q: Solve the following M_Technique. Max Z= 2x1 +3x2-4x3 Subject to x1+x2+x3=8 2x1-5x2+x3=10 x1,x2,x3>=0
A: Please follow the attached documents:
Q: An operations research analyst for a communications company has the following LP problem and wants…
A: Given, Max Z = 50X1 + 20X2S.T: 2X1 + X2 < 200X1 + X2 < 350Xl + 2X2 < 275
Q: Illustrate through your own example degeneracy in transportation problems. Can the optimal solution…
A: The question is related to Transportation Problem. Degenracy in a transportation occurs when the…
Q: 1. Maximize Z = 2X1 + X2 Subject to: X2 < 10…
A: Note: “Since you have asked multiple questions, we will solve the first question for you. If you…
Q: Consider the following linear program: Max 3A + 3B S.t. 2A + 4B 0 Find the Optimal Solution using…
A: Point X coordinate (A) Y coordinate (B) Value of the objective function (Z) O 0 0 0 A 0 3 9 C…
Q: Consider the followingg linear programming problem: Max 3A + 3B st. 2A + 4B ≤ 12 6A + 4B ≤ 24…
A: There are four extreme points for this solution. They are (0,0), (4,0), (0,3), (3,1.5)
Q: max z = 2x1 + 2x2 %3D x¡ + x2 < 6 2x, + x2 < 13 s.a. toda X; 2 0
A: Linear programming (LPP) is subject to linear restrictions. To put it another way, linear…
Q: Find the minimum cost.
A: Linear programming is a technique used to maximize or minimize the set of given variables. These…
Q: Considering the equations shown in figure below as constraints. Determine the optimum solution of…
A: Note: - Since we can answer only up to 3 subparts, we will answer subpart a, b, and c for your…
Q: Which of the following is not involved in a linear programming problem? a. variable b. solution set…
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Explain the kinds of problems that linear programming address
A: Linear programming is an operations research technique for maximizing resource utilization. The…
Q: Instructions: Solve using Excel Solver. Create the linear programming model and get the optimal…
A: Decision Variables: Suppose, x be the amount of product x1 and y be the amount of product…
Q: Explain all the steps when implementing the Branch and Bound method for the following optimization…
A:
Q: Use the simplex method to maximize the given function. Assume all variables are nonnegative.…
A: Given LP-Max f= 7x+14y +4zSubject to-3x+5y+4z≤303x+2y≤ 4x+2y≤ 8x,y,z≥0
Q: Maximize C = 13x + 3y subject to 12x + 14y ≤ 21 15x + 20y ≤ 37 and x ≥ 0, y ≥ 0. What is the…
A: Linear programming is a mathematical technique that is also used in operations management…
Q: Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3…
A: The concept applied here is of algebraic equations.
Q: The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At…
A:
Q: Given this linear programming model, solve the model and then answer the questions that…
A: Formula:
Q: Set up the simplex matrix used to solve the linear programming problem. Assume all variables are…
A: Objective Functions and Constraints: Based on the given details, the objective…
Q: Which of the following linear programming model has bounded feasible region? O max z= 3x + 2y…
A: The question is related to Linear Programming.
Q: Set up the simplex matrix used to solve the linear programming problem. Assume all variables are…
A: Given LP- Maximize f = 8x + 9y + 3zsubject to-2x + 7y + 8z ≤ 1006x + 3y + z ≤ 1603x +…
Q: Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Minimize z = x…
A:
Q: 2. Solve the following problem using graphical method. Show all the feasible solutions and obtain…
A: Given data, Min Z = 2x1 + 9x2 Subject to constraints 2x1 + 2x2≥15 0x1 +4x2 ≤45 0x2 + 3x2 ≤80…
Q: Consider the followingg linear programming problem: Max 3A + 3B st. 2A + 4B ≤ 12 6A + 4B ≤ 24…
A:
Q: between the left and right sides of a constraint. b. is the amount by which the left side of a ≤…
A: Answers are given below:
Q: Solve by the Big M – method: Maximize Ζ= x1 + 2x2 −3x3 + x4…
A:
Q: A plant has four operators to be assigned to four machines. The time (minutes) required by each…
A: When workers are assigned to certain duties based on cost, the Hungarian algorithm is beneficial for…
Q: 1. A specific assignment of values to decision variables is called what? a. Constraint…
A: Decision Variables: These are the unknown quantities that the LPP solution is supposed to estimate…
Q: A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit…
A: Given, Product Line 1 Line 2 A 12 4 B 4 8 Total hours 60 40
Q: Consider the followingg linear programming problem: Max 3A + 3B st. 2A + 4B ≤ 12 6A + 4B ≤ 24…
A:
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?
- Solve using the duality linear programming method of the following problem:Object Function: F = X1+X2+4X3Subjected to:X1+2X2+3X3 ≥ 1152X1+X2+8X3 ≥ 200X1+X3 ≥ 50X1,X2, X3 ≥ 0Solve the following problem with Excel Solver:Maximize Z = 3X + Y.1 2X + 14Y ≤ 85 3 X + 2Y ≤ 18Y≤ 4Consider the following primal LP problem:Maximize X1 + 2X2 – 9X3 + 8X4 – 36X5Subject to 2X2 – X3 + X4 – 3X5 ≤ 40 X1 – X2 + 2X4 – 2X5 ≤ 10 X1 ≥ 0, X2 ≤ 0, X3 ≥ 0, X4 ≥ 0, X5 ≥ 0 (a) Write the dual of the LP above, using variables Y1, Y2, etc.(b) Sketch the feasible region of the dual LP in 2 dimensions, and use the graphical method to find the dual optimalsolution (Plot an isovalue line corresponding to the feasible solution, move the line in improving direction, findthe last one touching the feasible region, and any point(s) on the intersection of the last isovalue line andfeasible region are optimal solutions)(c) Using complementary slackness conditions, - write equations which must be satisfied by the optimal primal solution X* - which primal variables must be zero?(d) Using the information in (c), determine the optimal primal solution X* (e) Compare the optimal objective values of the primal and dual solutions
- Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________Solve using the simplex method the following problem:Maximize Z=3X1 + 2X2 subject to: 2X1+ X2 ≤ 18 2X1 + 3X2 ≤ 42 3X1 + X2 ≤ 24 X1 ≥ 0 , X2 ≥ 0Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) 5X + 4Y ≤ 50 (4) 5X - 2Y ≤ 20 If constraints (3) and (4) are binding, what is the optimal solution (X, Y)? Answer choices (6, 5) (9, 5) (0, 20) (20, 0)
- Find the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x + 5y ≤ 12 6x + 2y ≤ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? (Round your answer to 3 decimal places.) What is the maximum value of the objective function? (Round your answer to 3 decimal places.)Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 8x + 8y subject to 7x + 9y ≥ 16 10x + 10y ≥ 22 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the minimum value of the objective function?