Thanks, @Markiyan Hirnyk and @Carl Love for your reply.

If it is assumed that m and n are both strictly positive, does the system {Fn,Fm} has real solution?

Great thanks!

Thanks, @Markiyan Hirnyk and @Carl Love for your reply.

If it is assumed that m and n are both strictly positive, does the system {Fn,Fm} has real solution?

Great thanks!

Hi, I cannot solve the 2 implicit functions with 2 unknown (m,n) simultaneously (please see attached maple file). Note: m and n are real numbers.

Download Question.mw

May I get some advice please? Many thanks.

Hi,

When I first tried to solve the equation, EQN, by following the method below, it worked, ie., EQN can be solved. But when I tried to solve the same equation again using the same method as below, the equation EQN, cannot be solved now! I wonder why. It is strange.

Digits := 20;
EQN := 5.915635290*10^18905*n*(ln(expand(.1974600000*(4.137221948*10^9-3.187977881*10^9*n+
3.579712132*10^9*n*taum+2.049414400*10^9*n*taut-5.560674900*10^9*taum-5.560674900*10^9*taut))/
(-2.065539727*10^9*n+2.333329620*10^9*n*taum+1.372164917*10^9*n*taut+2.519530558*10^9-
3.492604298*10^9*taum-3.723094273*10^9*taut))/((5.012372749*10^6989-
1.379404981*10^6989*n)^evalf(7447/10000)*taum))^evalf(10000/2753)-319.9820565*
ln((19746.*(4.137221948*10^11-3.187977881*10^11*n+3.579712132*10^11*n*taum+
2.049414400*10^11*n*taut-5.560674900*10^11*taum-5.560674900*10^11*taut))/
(-2.065539727*10^16*n+2.333329620*10^16*n*taum+1.372164917*10^16*n*taut+
2.519530558*10^16-3.492604298*10^16*taum-3.723094273*10^16*taut))/taum = 0;
#smoothed-out code: expand in logarithm and evalfed exponents
UUU := solve(EQN, n, useassumptions)assuming 0 < taut, taut < 1, taum > 0, taum < 1;

Thanks in advance for any kind advice!

Hi,

When I first tried to solve the equation, EQN, by following the method below, it worked, ie., EQN can be solved. But when I tried to solve the same equation again using the same method as below, the equation EQN, cannot be solved now! I wonder why. It is strange.

Digits := 20;
EQN := 5.915635290*10^18905*n*(ln(expand(.1974600000*(4.137221948*10^9-3.187977881*10^9*n+
3.579712132*10^9*n*taum+2.049414400*10^9*n*taut-5.560674900*10^9*taum-5.560674900*10^9*taut))/
(-2.065539727*10^9*n+2.333329620*10^9*n*taum+1.372164917*10^9*n*taut+2.519530558*10^9-
3.492604298*10^9*taum-3.723094273*10^9*taut))/((5.012372749*10^6989-
1.379404981*10^6989*n)^evalf(7447/10000)*taum))^evalf(10000/2753)-319.9820565*
ln((19746.*(4.137221948*10^11-3.187977881*10^11*n+3.579712132*10^11*n*taum+
2.049414400*10^11*n*taut-5.560674900*10^11*taum-5.560674900*10^11*taut))/
(-2.065539727*10^16*n+2.333329620*10^16*n*taum+1.372164917*10^16*n*taut+
2.519530558*10^16-3.492604298*10^16*taum-3.723094273*10^16*taut))/taum = 0;
#smoothed-out code: expand in logarithm and evalfed exponents
UUU := solve(EQN, n, useassumptions)assuming 0 < taut, taut < 1, taum > 0, taum < 1;

Thanks in advance for any kind advice!

Hi all,

Thanks very much for all the advice given.

I have attached the worksheet here for your kind reference.

FYI, pls: n (together with M, p, Y, and K) need to be solved as functions of taut, taum and parameters, and they will be substituted into the equation, V, to solve for optimal taut and taum to maximize equation V. Please kindly see the worksheet for the details.

Your advice and help would be greatly appreciated! 

opt_delta_.mw

Hi Kamel,

Many thanks and my doubt is now cleared!

Hi Kamel,

Many thanks and my doubt is now cleared!