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?I1I2 23 S1 S2$3SA$1-2 011000382 3 0-2 01206121 1-3 00102SA-3 0200-114-2-2 011 0 0 -4 0-8

Please refer below page.If you have any doubts please feel free to ask.Explanation:Step 1: Step 2:…

Answered: 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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List all the corner points for the collection of constraints of the linear programming problem Show your work!
(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.
Find out if it’s a linear program or not if it reformulate it in standard inequality form.
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
+ 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)
2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X1 x2 X3 S1 S2 S3 S4 55 S1 -2 0 1 10 0 0 3 3 0 -20 1 2 0 6 ུཚ་ 1 1 -300 1 0 2 -30 2 0 0 -1 1 4 -20 11 00-40-8

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