Results 1 to 5 of 5

Math Help - optimization

  1. #1
    Newbie
    Joined
    Oct 2007
    From
    Manchester
    Posts
    6

    optimization

    hello,

    i have a little question to ask, so here it is,

    "A consumer has 60 to spend on purchases of two goods with prices 5
    and 10. If x is the quantity of the first good bought then the quantity of
    the second good that can be bought is y = (60 􀀀 5x)=10 = 6 􀀀 0:5x. The
    consumer0s preferences are represented by the utility function
    u(x; y) = ln(x) + 2 ln(y) = ln(x) + 2 ln(6 􀀀 0:5x)
    Find that x which is the global maximum of this function. Justify your
    answer."

    when i do this question i keep getting a negative answer which seems wrong, people can't buy negative amounts of stuff.

    (hello bye the way, its my first post so hello all)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by happyhudson View Post
    hello,

    i have a little question to ask, so here it is,

    "A consumer has 60 to spend on purchases of two goods with prices 5
    and 10. If x is the quantity of the first good bought then the quantity of
    the second good that can be bought is y = (60 �� 5x)=10 = 6 �� 0:5x. The
    consumer0s preferences are represented by the utility function
    u(x; y) = ln(x) + 2 ln(y) = ln(x) + 2 ln(6 �� 0:5x)
    Find that x which is the global maximum of this function. Justify your
    answer."

    when i do this question i keep getting a negative answer which seems wrong, people can't buy negative amounts of stuff.

    (hello bye the way, its my first post so hello all)
    Could you please edit this to use only standard ASCII characters, so we
    don't have to guess what you are asking.

    Use + for addition, - for subtraction, * for multiplication and / for divisions,
    ^ to indicate raising to a power, and sufficient brackets to make the meaning clear.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    From
    Manchester
    Posts
    6
    sorry about that, i didn't check to see if it came out alright.

    "A consumer has 60 to spend on purchases of two goods with prices 5
    and 10.
    If x is the quantity of the first good bought then the quantity of
    the second good that can be bought is y = (60-5x)/10 which can be re written as y = 6- 0.5x.

    The consumers preferences are represented by the utility function
    u(x,y) = ln(x) + 2 ln(y) which can be rewritten as u(x)= ln(x) + 2 ln(6- 0.5x)

    Find the value of x which is the global maximum of this function"

    (and i only just noticed the edit button...never mind)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by happyhudson View Post
    sorry about that, i didn't check to see if it came out alright.

    "A consumer has 60 to spend on purchases of two goods with prices 5
    and 10.
    If x is the quantity of the first good bought then the quantity of
    the second good that can be bought is y = (60-5x)/10 which can be re written as y = 6- 0.5x.

    The consumers preferences are represented by the utility function
    u(x,y) = ln(x) + 2 ln(y) which can be rewritten as u(x)= ln(x) + 2 ln(6- 0.5x)

    Find the value of x which is the global maximum of this function"

    (and i only just noticed the edit button...never mind)
    A global maximum of:

    <br />
u(x)= \ln(x) + 2 \ln(6- 0.5x)=\ln(2x(6-0.5x))<br />

    Is also a global maximum of:

    <br />
U(x)= 2x(6-0.5x)<br />

    This is either a calculus type maximum where U'(x)=0 at an interior point of the feasible region [0,12] or occurs at an end point of this interval.

    Put:

    <br />
U'(x) = 2(6-0.5x)-x = 0<br />

    this has an extremum at x=6 and the second derivative test tells us this is a local maximum. At the end points of [0,6],\ U(x)=0 so x=6 is corresponds to the global maximum.
    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2007
    From
    Manchester
    Posts
    6
    thank you for the help, its always nice to have someone else go over a question, i never thought of just putting the 2 lns together i just differentiated both straight off and went from there. so thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. optimization help!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 12th 2009, 01:54 AM
  2. Optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2009, 03:09 PM
  3. Optimization
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2009, 11:56 AM
  4. optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 12th 2008, 11:47 AM
  5. Optimization
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: October 13th 2008, 07:44 PM

Search Tags


/mathhelpforum @mathhelpforum