using solver to complete a table

[justhrowit]

I've been taking some econmics 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(raised to 4th power)XM(raised to 6th
power)...sorry don't know how to type in exponents.

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?

Thanks in advance!

 

[justhrowit]

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

 

[justhrowit]

just want to bring this to the top!

 

[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.

 

[justhrowit]

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