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Expert: Alon Mandes - 9/17/2009


Question
I need help with two problems. The first is: maximize the utility function f(x)= log(x) over x^4.

The second problem is maximizing this utility function: U(x,y)=x^9, y^8 subject to the constraint x+4y=170.

Part b to the problem is to redo part a for U(x,y)= 27 log(x) + 24 log(y).

Thank you if you could help

Answer
In this case, the constrain can be substituted directly to U(x,y). There is no need for
"Lagrange Multipliers" . If x+4y=170 then x=170-4y . Now our function  U(x,y)=27Ln(x)+24Ln(y)
will become : U(y)=27Ln(170-4y)+24Ln(y). U'(y)=-4*27/(170-4y)+24/y. We now solve : U'(y)=0 :
27/(170-4y)=6/y --> (10-4y)/27=y/6 --> 0.37-0.14y=0.16y --> 0.3y=0.37 --> y=1.23
This is the stationary point. You may proceed %26 calculate x %26 U(x,u) .

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

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M.A in Mathematics & Bs.c in Electronics.

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