Author 
Comment/Response 
Ilya

06/10/04 07:03am
Hello all,
I am in a clinch with the following problem. I am trying to solve simple optimization problem using Mathematica:
The function is
Y=Y(x1,x2) = Exp[x1a1S1  x2a2s2]q1q2 + Exp[x1a1s1  x2b2S2] + Exp[x1b1s1x2a2s2] + Exp[x1b1s1x2b2s2]. Where xi, ai, si, pi  constants.
To find the infinum one have to solve system of equations dY/dx1=0, dY/dx2=0.
The most rediculus point is that I can solve it manually with simple substitution but the Great Mathematica returns me the error: "The equations appear to involve the variables to be solved for in an essentially nonalgebraic way." How can it be?
Could you please help me to solve this puzzle? How to solve this system in Mathematica!!!??? Supporting code would be greately appretiated!
Here is the code I use (with slight different and more attractive notation then I used above). Just copy and paste it in your wolfram software:
\!\(SetAttributes[{a\_1, a\_2, b\_1, b\_2, S\_1, S\_\(\(2\)\(\ \)\), \ q\_1,
q\_2, \ p\_1, p\_2, \ A, B, C, D}, \ Constant]\[IndentingNewLine]
Y\ = \ Exp[\(\[Gamma]\_1\) \(a\_1\) S\_1  \ \(\[Gamma]\_2\) \(a\_2\)
S\_2] \(q\_1\) q\_\(\(2\)\(\ \)\) + \
Exp[\(\[Gamma]\_1\) \(a\_1\) S\_1  \ \(\[Gamma]\_2\) \(b\_2\)
S\_2]\ \(q\_1\) p\_2\ + \
Exp[\(\[Gamma]\_1\) \(b\_1\) S\_1  \ \(\[Gamma]\_2\) \(a\_2\)
S\_2] \(p\_1\) q\_2\ + \
Exp[\(\[Gamma]\_1\) \(b\_1\) S\_1  \ \(\[Gamma]\_2\) \(b\_2\)
S\_2]\ \(p\_1\) p\_\(\(2\)\(\ \)\)\[IndentingNewLine]
Solve[{D[Y, \[Gamma]\_1] == 0, \
D[Y, \[Gamma]\_2] ==
0}, {\[Gamma]\_2, \[Gamma]\_1}\ ]\ /; \ {\(p\_1\)
b\_1/\((\(q\_1\) a\_1)\) == 1\ }\)
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