Problem in Solver

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J. Wang

I tried to solve the system
max -48.0204029083251a + 0.561454772949261b
st. 5.25111389160165a -15.6617965698242b <=0
a, b >=0
The solution for it should be not conveged. But the solver
told me that there is a solution, which is a and b are
euqal to zero. I tried in Excel 2003 and 2002, and both
have such problem. I am not sure whether it is a bug. Has
anybody experienced such thing?

Thanks,

J. Wang
 
I tried to solve the system
max -48.0204029083251a + 0.561454772949261b
st. 5.25111389160165a -15.6617965698242b <=0
a, b >=0
The solution for it should be not conveged. But the solver
told me that there is a solution, which is a and b are
euqal to zero. I tried in Excel 2003 and 2002, and both
have such problem. I am not sure whether it is a bug. Has
anybody experienced such thing?

Thanks,

J. Wang
Click to expand...
 
I tried to solve the system
max -48.0204029083251a + 0.561454772949261b
st. 5.25111389160165a -15.6617965698242b <=0
a, b >=0
The solution for it should be not conveged. But the solver
told me that there is a solution, which is a and b are
euqal to zero. I tried in Excel 2003 and 2002, and both
have such problem. I am not sure whether it is a bug. Has
anybody experienced such thing?
Click to expand...

Sorry for preceding blank response.

You want the values of a and b that produce the largest possible value for

-48.0204029083251 a + 0.561454772949261 b

subject to the conditions that 5.25111389160165 a - 15.6617965698242 b <=0 and
a and b >= 0. The first of these conditions may be rewritten as

5.25111389160165 a <= 15.6617965698242 b

which may be reduced to

a <= 2.9825665360016 b

If a were any small positive value, b could tend towards infinity, and both
conditions would be satisfied, and there'd be no upper bound on your objective
function, so no finite solution. Solver is thus doing the right thing saying
that it can't converge on a solution. That it sets a and b both to zero as a
'solution' is questionable, but since no useful solution exists no harm done.

In general, there's never any way to solve for extreme values of linear
objective functions without having your independent variables constrained to a
region of 2-space bounded on the 'side' on which the objective function is
increasing. The problem with your constraints is that they include the region in
the first quadrant of the a-b cartesian plane on and above the line defined by
a = 2.9825665360016 b and right of the vertical (b) axis. There's no constraing
on how large a and b can get.

*YOU* need to alter the problem so that you're giving Solver a system that *CAN*
be solved.
 
Don't know, but Excel XP tells me "The Set Cell values do not converge",
which is true because the problem is unbounded. For me, the value Solver
initially stops at is when A=0, and B is a large number. (B is unbounded).
Don't know how you have it set up, but Solver does not return 0 & 0 for me.
 
If a were any small positive value, b could tend towards infinity, and both
conditions would be satisfied, and there'd be no upper bound on your objective
function, so no finite solution. Solver is thus doing the right thing saying
that it can't converge on a solution. That it sets a and b both to zero as a
'solution' is questionable, but since no useful solution exists no harm done.
Click to expand...


I think that was the OP's point. If you propose an initial guess of
a=b=0, Excel 2002 erroneously concludes that the problem is solved by
that initial guess, instead of recognizing that there is no solution.

Jerry
 
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