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.maximize2x1 + x2+3x3subject tox2-x32,1+3x2+2x3 ≥ 3,2x1 +22+3 = 4,x1, x2, x3 0.

The first phase of the 2-phase simplex algorithm reveals that the given linear program is…

Answered: 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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Please show work and I will upvote for the correct answer. Any help is appreciated! Consider an ocean with x 2 4 islands, some of which are connected by bridges. A group of one or more islands form a Coalition if it's possible to travel between any of the island(s) in the Coalition using bridges. These Coalitions are also as large as possible. Among these x islands, there are x – 2 Coalitions. For example, for the case where x = 5→ there would be k – 2 = 3 Coalitions. In this example, there would be 3 coalitions with 2 islands-2 island-1 island, or 3 islands-1 island-1 island. Determine the maximum number of bridges that can exist among these islands and prove your answer.
For the following set of points, describe how the closest-pair algorithm finds a closest pair ofpoints: (1, 2), (2,−1), (3,−3), (3, 2), (−3, 4), (−1, 2), (2, 3), (1, 1), (−5,−2)
You know you have 5 pairs of sock in the laundry basket. You want a pair of matched socks but can’t see any socks. You reach into the basket and pull out socks. What’s the maximum of number of socks that you will have to pull out in order to guarantee that you will get a matching pair of socks?
When deleting a basic variable xBr from the simplex tableau, would it be possible to make xBr nonbasic by pivoting on any non-zero element in row r? What difficulties one might encounter with this approach?
A manufacturer of skis produces two models: a regular ski and a slalom ski. A set of regular skis produces a $25 profit and a set of slalom skis produces a profit of $50. The manufacturer expects a customer demand of at least 200 pairs of regular skis and at least 80 pairs of slalom skis. The maximum number of pairs of skis that can be produced by this
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.
Find the Ualue of x 2axt2 + 2 X+3
You, Alice and Bob are engineering a solution the Really Hard Problem and have come up with ten algorithmic solutions. Alice has analysed the code and expressed the run times of the ten solutions with the following ten functions: •fo(n) = (3n+3)³ • fi(n) = [₁2² f2(n) = n². (22+75) • f3(n) = 3log, n • f4(n) = fs(n) = log₂ (n^²) • fe(n) = log₂ (n² +5n-3) • fr(n) = log₂ (log₂ n+3) f8(n) = 2 f9(n) = 2222 a) Alice has asked you to help her classify these functions based on their asymptotic growth rate. That is, she wants you to prove a tight big-Theta bound for each function by following these steps. i. Use algebra to simply the function for ease of analysis. Remember the goal of simplification is to isolate terms and identify the dominant term. For instance, we might want to expand (n + 1)² to n² +2n+ 1 to see that n² is the dominant term. ii. Use your intuition, the limit test, or algebra to come up with a good guess of a tight bound. For instance, after isolating n² as the dominant term…
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
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