Consider the optimization problem of the objective function f(x, y) = 3x 2 − 4y 2...

Consider the optimization problem of the objective function f(x, y) = 3x 2 − 4y 2 + xy − 5 subject to x − 2y + 7 = 0. 1. Write down the Lagrangian function and the first-order conditions. 1 mark 2. Determine the stationary point. 2 marks 3. Does the stationary point represent a maximum or a minimum? Justify your answer.

Expert Solution

Colby Messinger answered 2 years ago

Maximize objective function P=3x+4y subject to: x + y ≤ 7 x ≥ 0 x+4y ≤...

Maximize objective function P=3x+4y subject to: x + y ≤ 7 x ≥ 0 x+4y ≤ 16 y ≥ 0

Maximize / minimize f(x,y) = 3x+4y subject to x^2 + y^2 = 25

Consider the following function: f (x , y , z ) = x 2 + y...

Consider the following function: f (x , y , z ) = x 2 + y 2 + z 2 − x y − y z + x + z (a) This function has one critical point. Find it. (b) Compute the Hessian of f , and use it to determine whether the critical point is a local man, local min, or neither? (c) Is the critical point a global max, global min, or neither? Justify your answer.

Undetermined Coefficients: a) y'' + y' - 2y = x^2 b) y'' + 4y = e^3x

Undetermined Coefficients: a) y'' + y' - 2y = x^2 b) y'' + 4y = e^3x c) y'' + y' - 2y = sin x d) y" - 4y = xe^x + cos 2x e) Determine the correct form of a particular solution, do not solve y" + y = sin x

Consider f(x) = 2 + 3x^2 − x^3

Consider f(x) = 2 + 3x2 − x3 a) Find local max and min values b) Find intervals of concavity and infection points

(6) Consider the function f(x, y) = 9 − x^2 − y^2 restricted to the domain...

(6) Consider the function f(x, y) = 9 − x^2 − y^2 restricted to the domain x^2/9 + y^2 ≤ 1. This function has a single critical point at (0, 0) (a) Using an appropriate parameterization of the boundary of the domain, find the critical points of f(x, y) restricted to the boundary. (b) Using the method of Lagrange Multipliers, find the critical points of f(x, y) restricted to the boundary. (c) Assuming that the critical points you found were...

Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The...

Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0, 0) is a stationary point of f. For what values of k will f have a local minimum at (0, 0)? (a) |k| > 4 (b) k ≥ −4 (c) k ≤ 4 (d) |k| < 4 (e) none of the above The point P : (2, 2) is a stationary point of the function f(x, y) = 6xy − x ^3...

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does...

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Consider the function y = f(x) = 2x3 − 3x2 − 9x − 2. (a) [2]...

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Problem 2. Consider the linear (perfect substitutes) production function f(x, y) = 12.7x + 19.4y. (A)...

Problem 2. Consider the linear (perfect substitutes) production function f(x, y) = 12.7x + 19.4y. (A) How many units of good y would be a perfect substitute for 1 unit of good x? What is the slope of the firm’s isoquants? (B) Suppose the input prices are (px, py) = (5, 8). What is the slope of the isocost lines? How much output does the firm get when it inputs $1 worth of good x? How much output does the...

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