consumer’s utility function is given by U=2*x*y+3*x where x and y denote the number of items of two goods (good 1 and good 2) that are bought. Each item costs €1 for good 1 and €2 for good 2. The consumer’s budget per day is €95, which is x+2y=95. If we use the Lagrange multiplier method to maximize the level of utility per day subject to that constraint. Find the values of “x” and “y” which maximize the level of utility subject to that constraint.

consumer’s utility function is given by U=2xy+3*x where x and y denote the number of items of two goods (good 1 and good 2) that are bought. Each item costs €1 for good 1 and €2 for good 2. The consumer’s budget per day is €95, which is x+2y=95. If we use the Lagrange multiplier method to maximize the level of utility per day subject to that constraint. Find the values of “x” and “y” which maximize the level of utility subject to that constraint.

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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Question

A consumer’s utility function is given by

U=2*x*y+3*x

where x and y denote the number of items of two goods (good 1 and good 2) that are bought.

Each item costs €1 for good 1 and €2 for good 2. The consumer’s budget per day is €95, which is x+2y=95.

If we use the Lagrange multiplier method to maximize the level of utility per day subject to that constraint.

Find the values of “x” and “y” which maximize the level of utility subject to that constraint.

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