2. Apply the first phase of the 2-phase simplex algorithm to the following linear pro-gramme giving the initial tableau and each further tableau produced. Give thestarting tableau for the second phase if there is one.maximize 2x1 x23x3subject toX2- x3 ≤ 2,x13x2+2x3 ≥ 3,2x12x2 x3 = 4,x1, x2, x3 0.

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

Answered: 2. Apply the first phase of the 2-phase…

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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First 3 parts are solved. 5-28 Consider the linear programmax x1 + x2s.t. x1 + x2 ≤ 9-2x1 + x2 ≤ 0x1 - 2x2 ≤ 0x1, x2 ≥ 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the modelin standard form.(c) Apply rudimentary simplex Algorithm 5Ato compute an optimal solution to yourstandard form starting with all slacks basic.(d) Plot your progress in part (c) on thegraph of part (a).(e) How can the algorithm be making progress when l = 0 if some moves of part(c) left the solution unchanged? Explain.5-29 Do Exercise 5-28 for the LPmax x1s.t. 6x1 + 3x2 ≤ 1812x1 - 3x2 ≤ 0x1, x2 ≥ 0
Apply the backflow algorithm to the digraph below T9 (6) T5 (12) T1 (3) T6 (10) T8 (4) T10 (5) Т2 (2) End ТЗ (8) T7 (9) T4 (11) Task 5 has a critical time of Task 2 has a critical time of
What is the use of the Euclidean algorithm?
Solve this using simplex algorithm
max 6x1 – 5r2 + 13 s.t. – r1 – 2x2 + 2r3 –30 I1 >0 I3 urs (a) Convert the LP to standard form. (b) Perform the first two iterations of the Simplex algorithm. Clearly indicate the enter- ing/leaving variables and the basic feasible solutions you find.
A monkey has filled in a 3 × 3 grid with the numbers 1, 2, . . . , 9. A cat writes down thethree numbers obtained by multiplying the numbers in each horizontal row. A dog writesdown the three numbers obtained by multiplying the numbers in each vertical column.Can the monkey fill in the grid in such a way that the cat and dog obtain the same listsof three numbers? What if the monkey writes the numbers 1, 2, . . . , 25 in a 5×5 grid? Or1, 2, . . . , 121 in a 11 × 11 grid? Can you find any conditions on n that guarantee that itis possible or any conditions that guarantee that it is impossible for the monkey to writethe numbers 1, 2, . . . , n^2 in an n × n grid so that the cat and the dog obtain the same lists of numbers? Please provide a mathematically rigorous solution with proofs that could be understood by a person at a high school level.
4. Consider the following LP: max z = 6x1 + x2 X1 + x2 5 5 2x, + x2 < 6 st. X1,x2 2 0 (a) Solve this problem using the Simplex Algorithm and obtain the optimal tableau for this problem. (b) If we add a new variable x3 such that: max z = 6x1 + x2 + x3 X1 + x2 + ax3 S 5 2x, + x2 + bx356 X1, X2, X3 20 where a and b are scalar values, define the conditions under which the current basis stay st. optimal.
Consider the following LP: max (2z1 + 5z2) s.t. 3z1 + 2z2 0 (a) Solve the LP with the graphical method. (b) Place the model in standard form. (c) Use a simplex algorithm in tableau form and solve the LP.
What is the quotient (q) and the remainder (r) when a is divided by b in theDivision Algorithm a = −144, b = 7a = 1,089, b = 33
At Long John Silver’s (LJS), Platter 1 comes with 2 pieces of fish, 3 pieces of chicken, and 5 fried shrimp, while Platter 2 comes with 3 pieces of fish, 1 piece of chicken, and 8 fried shrimp. Platter 1 sells for 8 dollars and platter 2 sells for 10 dollars. If LJS has access to 1000 pieces of fish, 1200 pieces of chicken, and 2600 fried shrimp, what is the optimal number of platters LJS should make in order to maximize its profit? Note that the constraints relate to (please use these in order) fish, chicken, and shrimp. Note that problem 7 had three constraints (excluding the non-negativity constraints), and setting two pairs of those constraints to equality led to two extreme points on the feasible region. What INFEASIBLE point was at the intersection of the other pair of constraints? In the optimal solution to problem 7, the optimum was found at the intersection of two of the constraints that were not non-negativity constraints. Call these “binding” constraints. One of those…

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