2. Suppose that we are carrying out the simplex algorithm on a linear program instandard inequality form (with 3 variables and 4 constraints) and suppose that wehave reached a point where we have obtained the following tableau. Apply one morepivot operation, indicating the highlighted row and column and the row operationsyou carry out. What can you conclude from your updated tableau?X1x2 X3 S1 S2 S3 S455S1-2 0110 00330-20 1 206ུཚ་1 1-3001 02-30 2 0 0-114-20 1100-40-8

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Answered: 2. Suppose that we are carrying out the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A linear programming problem is one that is concerned with finding the [Select] of a linear [Select] z = ax + by, where a and b do not both equal zero, and the [Select] variables and y are subject to the [Select] in the form of linear inequalities and equations. In addition, they must satisfy the nonnegative constraints of a > 0 and y ≥ 0. z of the form
List all the corner points for the collection of constraints of the linear programming problem Show your work!
R.H.S X1 X2 Хз S1 S2 S3 -4 -3 12 1 4 9. 1 4 R.H.S X1 X2 X3 S1 S2 S3 1 In the following, two Consecutive simplex Tableaus for a linear programming problem are shown. What is the value of b. 지기23 4
'Solve the following linear programming problem using the graphical method. Max (Z)=5X₁+7X₂ Subjected to: 2X₁+3X₂< 18 X₁+X₂ ≤8 X₂<4 X₁, X₂ 20
(a) u want to send these shipments as cheaply as possible. Formulate this as a linear program ( do not need to formulate it is standard inequality form) (b) all is the same as (a) but that only 220L of important chemical A are now required at warehouse 1 or 2 for storage, the company must pay transportation costs or can be disposed of at the port in which case the company paus no transportation costs but pays a disposal fee of £16 per L. You want to find how to ship or dispose of all 610L of chemical imported at the mimimum cost while still ensuring that required amounts (220L and 330L respectively) delivered to warehouse 1 and 2. Describe how to modify your linear program from previous question.
Solve the following linear programs (LPs) using the simplex algorithm. • For each tableau you obtain, write the associated BFS and its objective value. • For each LP, find the complete optimal solution set and write it using appropriate mathematical notation. Use only the information in the tableaux to justify your answer. maximize z(x1, x2, x3) = subject to -2x1 + 4.x3 + 2.x3 0
Q6. Consider the following linear program in standard maximization form: -5 max{r1 – x2} subject to -4 X1, 12 a) Use the Simplex Method (as seen in class) to solve the above linear program. Be sure to: o Indicate all slack and artificial variables you introduce. o Indicate the objective S of the extended tableau. o Whenever your tableau is in RRREF, indicate the current solution's values for all vari- ables. o Before pivoting, indicate the entry you plan to convert to the next pivot. o Clearly indicate why you should stop the algorithm and give a precise conclusion. b) Draw the feasible region in a fairly large and well-scaled diagram. Determine the coordi- nates of each vertex and label the vertices of the feasible region in your diagram. c) Based on the graphical approach, describe the optimal solutions of this LP (if any). VI VI AI
The surface defined by z = f(x, y) = 2x + y hovers above the region defined by the graphic below. Find the total volume of the space above the region and below the surface. All distances are measured in feet. State whether you used Type 1 or Type 2 regions. A Type I region lies between two vertical lines and the graphs of two functions of x. Figure 15.2. 3: A Type II region lies between two horizontal lines and the graphs of two functions of y A Type I region lies between two vertical lines and the graphs of two functions of x. A Type II region lies between two horizontal lines and the graphs of two functions of y
+ 7. Consider the feasible region shown below. Assume the origin (A) is feasible and the constraints are all constraints and the variables are all nonnegative. Suppose you wish to maximize 1 + over this feasible region and you are currently at point G. Which variable should enter the basis in the first iteration of the simplex algorithm if we wish to maximize the objective function improvement after the first iteration? O only 2₂ only Ⓒ* only A 1.₂. or s 1 H B G A: (0,0,0) B: (1,0,0) C (0, 1, 0) D: (0, 0, 1)

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