The constraint 5x 1 − 2x 2 ≤ 0 passes through the point (20, 50). True False
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- A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤72 (C1) 1X1+2X2≤72 (C2) X1,X2≥0The optimal solution of a minimization problem is at the extreme point closest to the origin. Analyze this statement
- Use the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 2), (0, 3), (2, 2), (2, 0), (1, 1), (2, 1), (3, 3)}. (a) Draw the directed graph of R. (b) Is R reflexive? Explain. (c) Is R symmetric? Explain. (d) Is R transitive? ExplainWhich of the following is true regarding the linear programming formulation of a transportation problem that doesn't have any unacceptable routes? The number of constraints is calculated as number of origins times number of destinations. The constraints' left-hand-side coefficients are less than zero. The objective function value is either 0 or 1. The number of variables is calculated as number of origins times number of destinations.
- Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤100 (C1) 1X1+2X2≤100 (C2) X1,X2≥0 Part 2 The optimum solution is: Part 3 X1= ______ (round your response to two decimal places).Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.Suppose you own 11 bronze coins worth a total of $150,11 silver coins worth a total of $160, and 11 gold coinsworth a total of $170. Develop a linear integer model tofind a combination of coins worth exactly $110
- Vladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029 point, and drawing a game scores 12match point. After thetwo games are played, the player with more match points isdeclared the champion. If the two players are tied after twogames, they continue playing until someone wins a game(the winner of that game will be the champion). Duringeach game, Ulanowsky can play one of two ways: boldly orconservatively. If he plays boldly, he has a 45% chance ofwinning the game and a 55% chance of losing the game. Ifhe plays conservatively, he has a 90% chance of drawing thegame and a 10% chance of losing the game. Ulanowsky’sgoal is to maximize his probability of winning the match.Use dynamic programming to help him accomplish thisgoal. If this problem is solved correctly, even thoughUlanowsky is the inferior player, his chance of winning the match is over 12. Explain this…Consider the following all-integer linear program:max 5x1 + 8x2s.t. 9x1 + 4x2 ≤ 361x1 + 2x2 ≤ 10x1, x2 ≥ 0 and integer.Consider the points (0, 0), (1, 1), and (2, 3). Formulatean NLP whose solution will yield the circle of smallestradius enclosing these three points. Use LINGO to solvethe NLP.