Consider an optimization problem where we want to minimize:f (x1, 22, L3) = 100(x2 – a})² + (1 – x1)² + 100(x3 – x3)² + (1 – x2)?1. Compute the gradient Vf(x) and find optimality candidates (x¡, x;, x3).2. Compute the Hessian F(x) and check if the points from step 1 satisfy the second order optimalityconditions.

Step:-1 Given that fx1, x2, x3 =100x2-x122 + 1-x12 +100x3-x222 + 1-x22 Part (1):- differentiate f…

Answered: Consider an optimization problem where…

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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3. Suppose that a Pizza Store revenues about 20,000r pesos when employing y clerks. Let P be the weekly profit function (in pesos) of the store, which is given by P(r, y) = 3, 000 + 240y + 20y(x – 2y) – 10(r - 12)2. %3D What should be the number of clerks and their collected revenue to obtain the greatest profit" If the profit function is constrained by the equation 61r - y = 6133, is there still %3D any profit? Justify your answer.
[3.27] Consider the following problem: Maximize 2x₁ subject to X1 2x1 X1 X1, + x2 + 2x₂ + 3x2 x2, + 6x3 + 4x3 + x3 X3 X3, 11+ + 4x4 ********* X4 X4 ≤6 < 12 2 ≤ X4 X4 2 0.
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2. The Minimum point of y= 8x+4 (x-2)²
3. Suppose that a Pizza Store revenues about 20,000r pesos when employing y clerks. Let P be the weekly profit function (in pesos) of the store, which is given by P(r, y) = 3,000 + 240y + 20y(x – 2y) – 10(r – 12)*. What should be the number of clerks and their collected revenue to obtain the greatest profit? If the profit function is constrained by the equation 61x – y = 6133, is there still any profit? Justify your answer.
3. Suppose that a consumer has a utility function u(x1, x2) = x1 + x2. Initially the consumer faces prices (1, 2) and has income 10. If the prices change to (4, 2), calculate the compensating and equivalent variations. [Hint: find their initial optimal consumption of the two goods, and then after the price increase. Then show this graphically.] please do step by step and show the graph
c) A student wishes to allocate her available study time of 60 hours per week between two subjects in such a way as to maximize her grade average. She formulates two functions governing the grades of each module which can be taken as: 9₁ (t₁) = 20 + 20√₁, with t₁ > 0 and 9₂ (t₂) = -80 + 3t2, with t₂ > 80/3 maximize the grade average subject to the time constraint t₁ + t₂ = 60. You do not need to show that you have obtained a maximum.

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