Use Fourier-Motzkin elimination to give a linear combination of the following in- equalities that proves that there is no (r, y, z) satisfying all four inequalities. (a) (b) (c) (d) -x - y – 2z < -1 I-y -z -2 -r+y - z <-1 y + 3z <0

Q: 1. a. Show that this model has an unbounded solution by Big M Method. b. What can be changed to have…

A: According to the given information, it is required to first show that the given equation has…

Q: Suppose f(x) = x². You want to find a point at which this function is minimized %3D using the…

A: Step:-1

Q: Use partial fraction decomposition to evaluate the integral: 6r - 3 1² - dr = 2-r-20 Be sure your…

A: Topic = Integration

Q: 3. Let f(r, y) = y²x – yx² + xy. Find all critical points of f.

A: We have to determine critical points of f

Q: 2. Find the maximum of the function: f (x ) = -x* – 2x³ – 8x² – 5x a. Using Golden Section Search…

A: We have to find the  maximum of the function: The given function is f(x)=-x4-2x3-8x2-5x a. Using…

Q: b) Minimize the function f(x) = 4x + x²– 7x + 14 by using the Golden search method, in the interval…

A: Given function: fx=4x3+x2-7x+14 The interval given is 0,1. So, a=0, b=1. Using Golden search method,…

Q: %3D 1. Find the critical points forf (x) = 3x +

A:

Q: 3. Use Lagrange multipliers to find the extreme values of the function f(r, y, 2) = In(1 + 2²) +…

A: To find the extreme values of function  f(x,y,z)=ln(1+x2)+ln(1+y2)+ln(1+z2) subject to constraint…

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)=…

A: Definition of homogeneous function:- A function fx,y is said to be homogeneous if i an be written as…

Q: x+ y +z = 4 2x - 3y + z = 2 -x +2y - z =-1

A: Given, system if equations is-                       x+y+z=4                      2x-3y+z=2…

Q: J 3. Use a partial fractions decomposition to evaluate x² + 2 (x - 1)(x-4) (x + 2) -dx.

A:

Q: 7x2+3x+2 21 Express x+1)-(x-2) 7x2+3x+2 - as partial fractions. Hence, evaluate J, &+1<(x-2) dx

A:

Q: 2:2 39. - expressed in partial fractions where 1 - 4 P,Q and R are real constants with r +2, is A r…

A: Partial fraction

Q: a. Use the long division for solve (x - 7x -5x + 2)+(x-3). b. 30-5х Express as a partial fraction…

A: Follow step 2

Q: 2. Let f(x, y) =r² – 2xy + 2y² - x + 3. (a) Determine all the critical points of f. (b) Determine…

A:

Q: Find the first partial derivate with respect to x, y, and z. 1 G(x, y, z) = V1- x2 – y2 – z²

A: the solution is given below in step 2 and 3.

Q: 5. Consider the homogeneous case of the linear third-order Cauchy-Euler ODE, L[y] = a3x°y" + a2x²y"…

A:

Q: 2. Consider the quadratic function aT Ga+ba in four variables, where 2 -1 -1 2 -1 -1 G: 2 -1 -1 2…

A:

Q: (k+) > ミo Prove that <r for all K7/0 in the Steepest descent method.

A: To Prove- Prove that rk, rk+1 = 0 for all k ≥ 0 in the Steepest descent method.

Q: (a) -5x +2y+3z=-12 X-2y + 3z = 3 and X+ y+Z=2 levels perpendicular to the arachecite (intersection)…

A: Here we have been given two planes  x -2y +3z = 3 x + y +z = 2 These two planes intersect…

Q: 2х 6. Let f(x) = (x² +x+1)(x+3)²(x-3) The decomposition of f (x) into sum of partial fractions is: A…

A: The answer is found in step-2

Q: Write out the form of the partial fraction decomposition. (Do not find the numerical values of the…

A:

Q: 1. a. Show that this model has an unbounded solution by Big M Method.     b. What can be changed to…

A: 1. (a) Given,               Max Z=3x1+6x2subject to       3x1+4x2≥12    -2x1+x2≤4and      x1, x2≥0

Q: 6) Use Lagrange multiplier method to find the extrema of f(x1, Xz. -. , In) = x, + x2 + +x, subject…

A: Given, f(x1,x2,....xn)=x1+x2+x3+.....xn,  constraint x12+x22+x32+....+xn2=1 now equation we need to…

Q: (a) k : R³→ R defined by: k (x) = x" Ax + b, %3D where: 3 -1 1 A = –1 3 1 1 1 -3 and b = 2. Is k (x)…

A: (a) k:R3→R defined by  kx=xT Ax+b where A=3-11-13111-3 and b=2. is kx a quadratic form?

Q: (a) Starting from the initial trial solution (x1, x2) = (0, 0), apply the gradient search procedure…

A:

Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have given  y'=2x-3y+1   ,y(1)=6 we know that Euler's formula…

Q: (h) Write down the Lagrange's polynomial through (x), fo). (x1, f1), (x2, f2). Hence express 3x²…

A:

Q: Let f(x) = 6x²(x – 1) + 10. %3D Find the critical points c that correspond to local minima.

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: Consider the quadratic function Ga+ba in four variables, where 2 -1 -1 2 --(-:-) -1 -1 2 -1 -1 G = 2…

A: As per the question we are given a quadratic function in four variables as : (1/2)xTGx + bTx Where…

Q: 6.12 Consider the problem minimize f(æ) subject to x € N, where f: R? {x = [x1, c2]T : xỉ + *2 2 1}.…

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have to use the Euler method

Q: Jse Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: Given: dydx=2x-3y+1, y(1)=6 f(x,y)=2x-3y+1, x0=1, y0=6, h=0.1…

Q: Maximize P = xyz subject to x + z = 12, y + z = 12, x ≥ 0, y ≥ 0, and z ≥ 0

A:

Q: Find all critical points of f(x,y)=3x2+5xy+4y2.  If there are multiple critical points, separate…

A: to find:- critical points.

Q: -Find the least squares approxtmation polynomial of degree two for the continuous function f(x), (x)…

A: Least square method to approximate polynomial: Least square method to approximate the two degree…

Q: d. If x=c is an inflection point for f, then f(c) must be a local maximum or local minimum for f.…

A:

Q: minimize z -y+: subject to: r-y22 I- 2y <1 2 is unrestricted.

A: Given that min x-y+zs.t    x-y≥2       x-2y≤1       y+z≤1x,y≥0 and z isunrestricted

Q: 2/2 -irT b1 (r)e¬3iwT/2 + Ve-irT 2(r)e-biwT/2 V(x,T) = -irT %3D e 드n(x)e-(r+ ¥)T + 2/2 2(x)e-(r+)7…

A:

Q: Зx-1 (as a partial sum) (x2 – 1) Select one: a. B + х — 1 A D + (x – 1)? x +1 (x + 1)2 - - b. A D (x…

A:

Q: 2. Let f(r, y) = x² – 2xy + 2y² – x + 3. (a) Determine all the critical points of f. (b) Determine…

A:

Q: 3 -2 Find the minimum value of q(x) xT x subject to the condition ||x|| 1 %3D 1 Select one: O A. 2 -…

A: Introduction: The method of Lagrange multipliers is an approach for finding the local maxima and…

Q: The function f (x, y) = x³ + y³ + 3x² - 3y² - 8 has local minimum at the critical point (0, 2). True…

A: To tell if the given statement is true or false.

Q: 1. a. Show that this model has an unbounded solution by Big M Method. b. What can be changed to have…

A: Given Max Z = 3x1 + 6x2      Subject to 3x1 + 4x2 ≥ 12…

Q: Sketch the following problem graphically: max f X2 = X2 subject to g1 = x1 – (1 – x2)³ < 0 92 = X1 2…

A: Given - Sketch the following problem graphically. maxx2f = x2subject to g1 = x1 - 1 - x23 ≤ 0…

Q: 10. Consider the function f(x, y, z) = 6x² + 3y² + 2z². A. What is the minimum value of f if we…

A: function f(x, y, z)=6x2+3y2+2z2 we have to find maxima and minima using LaGrange multipliers method

Q: 25 2=9. - Maximize Q=xy, where x and y are positive numbers such that x +- and y = The maximum value…

A: