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using solver to complete a table

  1. #1
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    using solver to complete a table

    New here..please be gentle!

    I've been taking some economics classes. Our teacher has showed us some problems using solver to complete tables.
    Wondering if anyone out there can help.

    We have a company who uses units of labor (L) and material (m) to produce a certain quantity of output (q). The price of labor is $1 per unit of L and the price of materials is also $1 per unti of M.
    The prduction function is Q=(L^4)(M^6)

    Anyway, we're basically given a table (spreadsheet) with Q as the first column..labled 1 down to 9. Then column 2 is L, Column 3 is M, and then the final column is Total Cost.

    Basically, I'm trying to find the cost minimizing quantities of L and M that should be used to produce each quantity of output. So far, I've had little luck using calculus. How can this be done using solver?

    Q L M TC
    1
    2
    3
    4
    5
    6
    7
    8
    9


    Thanks in advance!
    Last edited by justhrowit; 02-09-2006 at 01:24 PM.

  2. #2
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    I've been playing with this a bit.
    I guess I'm just unsure on how to enter the formulas into the cells. I'm sure there are many other things I'm failing to comprehend here. I just end up getting 1 for all the cells.

    J

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    just want to bring this to the top!

  4. #4
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    Patience, it sometimes takes a while for these people to come up with solutions.

    I didn't find the calculus of this problem to be that difficult:
    TC=$1*M+$1*L
    Q=L^4*M^6
    L=(Q*M^-6)^1/4: Assume L must be >0 so that negative root is ignored.
    TC=$1*M+$1*(Q*M^-6)^1/4
    Take derivative, set equal to 0, solve for M, then obtain L from 3rd eqn, then check to make sure this represents a minimum.

    Solver can obtain the same results, it's just a little more tedious, because you either have to manually call solver for each row, or you need to write a VBA Sub procedure that will loop through the rows and call solver for you. Either way, the basic setup is:
    L=(Q*M^-6)^1/4
    M=initial guess for M
    TC=$1*M+$1*L
    Set solver to minimize TC by changing M.

  5. #5
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    HAHA...Patience has never been my strong suit! I'm going to hit this and see if I can get this to work! Your help is VERY MUCH Appreciated!

    Jay



    Quote Originally Posted by MrShorty
    Patience, it sometimes takes a while for these people to come up with solutions.

    I didn't find the calculus of this problem to be that difficult:
    TC=$1*M+$1*L
    Q=L^4*M^6
    L=(Q*M^-6)^1/4: Assume L must be >0 so that negative root is ignored.
    TC=$1*M+$1*(Q*M^-6)^1/4
    Take derivative, set equal to 0, solve for M, then obtain L from 3rd eqn, then check to make sure this represents a minimum.

    Solver can obtain the same results, it's just a little more tedious, because you either have to manually call solver for each row, or you need to write a VBA Sub procedure that will loop through the rows and call solver for you. Either way, the basic setup is:
    L=(Q*M^-6)^1/4
    M=initial guess for M
    TC=$1*M+$1*L
    Set solver to minimize TC by changing M.

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