Prove that y2 + y3 + 2y4 ≤ 6 is a valid Gomory cut for the following feasible region. X = {y ∈ Z+4 : 4y1 + 5y2 + 9y3 + 12y4 ≤ 34 }

Q: 32. Maximize and Minimize Z = 7x + 36y 2x + 3y > 6 -3x+ 4y < 8 5x – y < 15 Subject to :

A: We first draw 2x+3y=6 , -3x+4y=8 and 5x-y=15(using graphing calculator)

Q: Find the values of x, y that maximize 7 - 2x² - 2xy-1/²+2 +2x+6y X= subject to the constraint x+y=…

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Q: Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3) Let f:R - R be defined as: Vx = (x, X2, X) € R f(xi,X2, x3) = 7(x- x) + 3(1- x2) + 6x . a. Is f…

A: Given:Let f:R3→R be defined as: ∀x = (x1, x2, x3)  ∈ R3  f(x1, x2, x3) = 7(x1- x2)2 + 3(1 –x2 )2 +6…

Q: 1. Determine non-negative x and y that satisfy: X-4y<0 X- y<2 -2x+3ys6 20 y20 and a. Maximize f =…

A: Plot the constraints and obtain their point of intersection x-4y=0      (1) x-y=2        (2)…

Q: Consider the problem min (x³ + y³ + z³) s.t. x² +y? + z? = 1 (1) Is the feasible region of the…

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Q: Find the dimensions of the minimum-cost open-top rectangular tainer. (Let v* = 10 m³.) con-

A: Given. We need to find the dimension of a topless cuboidal container. Whose volume is 10m³ And…

Q: 1. Find the maximum of P-4x+5y subject to 2x+y10 x20, y20 Sketch your feasible region and find all…

A: The LPP is given as max P=4x+5y subject to 2x+y≤24x-y≥0x+2y≥10x≥0y≥0   We will solve it by Graphical…

Q: Which of the following points is a corner point in the feasible region for this LP problem? a.)…

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: Here is the table of distance between workstations: W1 W2 W3 W4 W5 W6 W1 0 10 20 30 30 20 W2 10 0 25…

A: Aim: To maximize the sum of three distances between them: To maximise :

Q: Use the following problem to answer questions 9 - 10. Minimize C-2x + 10y 5x 2y 2 x + 2y 40 20 9.…

A: We have given, constraint equations and a function that needs to be minimized.

Q: (T3-T) (Use Geogebra) Determine the feasible region and label the coordinates of the corner points.…

A: Given that, Maximize z = 120x1 + 100x2   subject to:   10x1+ 5x2 ≤ 80   6x1+6x2 ≤ 66   4x1+8x2 ≥ 24…

Q: Is this a linear optimization problem? Max Z = xy – 1 Subject to: x-y2 ≤ 5 0 ≤ y ≤ 3 x≤2

A: Consider the  standard Linear programming :  Max…

Q: Minimize: z = x - y subject to: 4х — Зу <0 x + y < 10 х, у 2 0

A: we will consider inequalities as equality and then draw the graph.

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Find the extreme values of g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of…

A: Given g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of Lagrange multipliers.

Q: Write the dual of the following LP pra lem Minimize Z = 3r- 2r2 + 4x3 Subject to the constraints 3r,…

A: Find dual from of the lp problemMIN z = 3x1 - 2x2 + 4x3subject to3x1 + 5x2 + 4x3 &gt;= 76x1 + x2 +…

Q: Use the method of Lagrange multipliers to find the maximum and minimum values of the function f(r,…

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Q: Use the method of Lagrange multiplier to determine the absolute maximum and minimum valeves of the…

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Q: 6. Eva wants to fence two rectangular plots of land. Both plots must have the same dimensions and…

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Q: For x,y,z > 0, use the Lagrange Multiplier Method to find the minimum value of 1 1 1 + + x y Subject…

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Q: 5. Use the method of Lagrange multipliers to minimize f (x, y) = x2 + y? subject to 2x + 8y 102.…

A: The given question is related with Lagrange multipliers . We have to minimize fx , y = x2 + y2…