Answered: Using Lagrangian Multiplier Method,…

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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• Use the method of Lagrange multipliers to solve optimization problems with one constraint. Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 80L0.84 K0.16 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $400 and each unit of capital costs $2,000. Further suppose a total of $250,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Units of labor, L = Units of capital, K = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production = units Question Help: D Video D Post to forum
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, у) = 4x + 8y, x² + y2 = 20 maximum value minimum value
Here is the original LP max z= 3x1 + 2x2 2x1 + *2 < 100 < 80 < 40 s.t. xi + x2 and the optimal tableau: S1 82 83 rhs 1 1 180 1 -1 2 60 -1 1 1 20 1 1 -1 0 20 Use decimals with no extra zero's: 1. What is the allowable increase for constraint 2 1 2. What is the allowable decrease for constraint 2 3. What is allowable increase for BV coefficient c2 4. What is allowable decrease for c2 5. Will {x2,s3, x1} be BV for a bfs if b2 is changed to 90 Y/N

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Using Lagrangian Multiplier Method, maximize the following utility function: U=2x+3y+ 3xy Subject the to following constraint: 2x+3y = 8 and find out optimal values of goods 'x' and 'y', where utility of the is consumer maximum?