## How do I solve non linear optimization problem and...

I want to maximize a total profit (TP) function which is dependent on five independent variables (E,W,T, theta, tp). All these five variables can have non negative values. The TP function is given below- ( first TP is directly copied from maple worksheet and than copied again as a picture for clear viewing).

TP = (p1*(Q-q)+p1*(1-theta)*(q-E)+s*E-c*Q-o-h*((1/6)*alpha*W^beta*a*p1^(-b)*tp^3/m-(1/2)*alpha*W^beta*a*p1^(-b)*tp^2+Q*tp)-(t1-tp)*h*((1/2*(-(2/3)*t1+m-(1/3)*tp))*W^beta*a*alpha*(t1-tp)*(-p1*(-1+theta))^(-b)+W*m)/m-(1/2)*h*(W+E)*(T-t1))/T-u*W

I am trying the maximize TP with respect to above five independent variables. I tried to solve  five equations ( representing first order partial derivative of TP with respect to each of the independent variables equated to zero) simultaneously by "solve" and "fsolve" command but both these commands fail to give any output. I have also tried three other commands in optimization package ( QPSolve, NLPSolve, Maximize) but all these three commands also doesn't give any output. I want to prove the concavity of TP function with respect to five independent variables, please guide how it can be done. ( I have computed the Hessian matrix but since five first order equations doesn't give output ( through fsolve command) so I am unable to compute Hessian at these first order optimiality condition solution.). The values of the paramters in the TP equation are -

[alpha = 50, beta = .7, c = 20, h = 4, m = .4, o = 10, p1 = 40, s = 10, u = 5, a = 15000, b = 2]

## Fourth order problem showing use midpoint method...

Dear sir,

I tried to solve a fourth order problem. But I got the error message as better to use midpoint method. Can I know what is midpoint method and here I uploading the problem please verify it if I did anything mistake?program.mw

## How can i get rid out of this error?...

restart;
with(plots); with(DEtools);
`&epsilon;` := .1;
de1 := x[0](t)+`&epsilon;`*x[1](t);
ode2 := sin(t)-`&epsilon;`*t*sin(t);
MODEL := {ode1, ode2};
VARS := {x(t), y(t)};
DOMAIN := t = 0 .. 20;
RANGE := x = -3 .. 3, y = -3 .. 3; COLORS := [BLACK, BLUE];
IC1 := [x[0](0) = 0, x[1](0) = 0]; IC2 := [(D(x[0]))(0) = 1, (D(x[1]))(0) = 0];
DEplot(MODEL, VARS, DOMAIN, RANGE, [IC1, IC2], stepsize = .1, arrows = THIN, linecolor = COLORS);
Error, (in DEtools/DEplot/CheckInitial) the 'number' option must be specified before initial conditions

## New to Maple. Trying to sovle 3rd order PDE system...

Hi I am new to Maple. I have 2 question:

1)I tried to run the following but I get this error as shown.pde1 is the PDE system. IBC, or you can refer bc1 to bc5 are the boundary condition given.

2)My bc4 & bc5 is suppose to be approaching 0 when y approch infinity  which is why I just put y to be equal to a large value while bc4 and bc5 equal 0. Do Maple have a function to use the approach method?

restart; with(PDEtools):

pde1 := [(x*y+1)*(diff(f(x, y), y, y, y))+(x+f(x, y))*(diff(f(x, y), y, y))-(diff(f(x, y), y))^2+g(x, y) = 0, (x*y+1)*(diff(g(x, y), y, y))+(x+f(x, y))*(diff(g(x, y), y))-(diff(f(x, y), y))*g(x, y) = 0];

IBC := [eval(f(x, y), y = 0) = 0, eval((D[2](f))(x, y), y = 0) = 0, eval(g(x, y), y = 0) = 0, eval((D[2](f))(x, y), y = 10000000000) = 0, eval(g(x, y), y = 10000000000) = 0];

bc1 := eval(f(x, y), y = 0) = 0

bc2 := eval((D[2](f))(x, y), y = 0) = 0

bc3 := eval(g(x, y), y = 0) = 0

bc4 := eval((D[2](f))(x, y), y = 10^10) = 0

bc5 := eval(g(x, y), y = 10^10) = 0

sol1 := pdsolve(pde1, [IBC], numeric, [f(x, y), g(x, y)], 'spacestep' = 0.1e-2, 'indepvars' = [x, y])

Error, (in pdsolve/numeric/process_IBCs) invalid initial/boundary condition: [f(x, 0) = 0, (D[2](f))(x, 0) = 0, g(x, 0) = 0, (D[2](f))(x, 1000000000000) = 0, g(x, 1000000000000) = 0]

## How to convert series functions back to it origina...

Good morning sirs,

Anyone with the idea(s) on how to convert series back to its original form should please share with me.

Take for example

a-(1/2)*beta*a^2*y^2+(1/24)*beta^2*a^3*y^4-(1/720)*beta^3*a^4*y^6+(1/40320)*beta^4*a^5*y^8-(1/3628800)*beta^5*a^6*y^10+(1/479001600)*beta^6*a^7*y^12-(1/87178291200)*beta^7*a^8*y^14+O(y^16)

is a series for a*cos(sqr(a*beta)*y)

## Maple and Geometry Expressions software...

Hi, is anyone using the Geometry Expressions software together with Maple? I've found about this software on forum and installed a free demo version. It is using symbolic geometry, which I haven't been able to find this feature on other software, and can work very well with Maple, but unfortunatelly, my demo version doesn't work properly, and their oficial website http://saltire.com/ has lots of errors 404 page not found. I have requested support, but have had no answer so far. I was so happy finding this software, but now I am thinking maybe wasting my time. If you are using it, or maybe think it would be good to give it a go, please let me know if it is working for you. A particular feature which is not working for me is 'creating angles'. Thank you.

## Multiplying numerator and denominator by the same ...

I have a fraction where I would like to isolate a certain term by multiplying the numerator and denominator by the same term.

My fraction is:

outOverin := R[2]*s^2*L[2]*C[2]/(s^4*C[2]*C[3]*L[2]*L[3]*R[2]+s^3*C[2]*L[2]*L[3]+s^2*C[2]*L[2]*R[2]+s^2*C[3]*L[2]*R[2]+s^2*C[3]*L[3]*R[2]+s*L[2]+s*L[3]+R[2])

I would like to take out a term so that I have s4 on its own in the denominator, so I try the following:

outOverin*(1/(C[2]*C[3]*L[2]*L[3]*R[2])*(C[2]*C[3]*L[2]*L[3]*R[2]))

But Maple does not take out the term like I would like it to, and I get the same fraction as before

How can I isolate s4 in the denominator?

## i cant draw a plot ...

hi
i want to draw a plot with to column-numerical that i imported from excel (i import one of the, for x axis and another for y axis)

## finding the area enclosed by a curve such as y=2x ...

Hi, I know the commands for when both curves/functions are y=....., but not when one of them is y=... and the other is a straight line going through the x-axis. I would like to be able to find the points of intersection in decimals, to plot them together such that I can see the points of intersection and finally I need to find he area enclosed between the two. Would appreciate your help.

## System of linear equations...

I have to find the tangent lines to the circle x^2+y^2+6*x-8*y+25 = 1/16 which pass at the O(0;0)

So i make a general line y=m * x

Ho can i put m*x instead of y in the circle and calculate the delta of the equation that i get?

## How to write a the iteration code in Maple...

Dears I have the following statment in Matlab

r=8;             ZUM=U(1)-YU(1);            IT=0;

for r=2:10

ZU(r)=abs(U(r)-YU(r));

if ZU(r)> ZUM

ZUM=ZU(r);

else

ZUM=ZUM;

end

end

ZUM;

while IT < 20

IT=IT+1

if ZUM < (0.1)^r

IT=20;

else

for r=1:Nx

YU(r)=U(r);

end

YU;

I need to write this statment in Maple

## How do i modify 3d plot axis?...

All the 3d plot in my maple are upside down.....the tickmarks..the numbering even the lebeling are also upside down...how do i solve it....plz help

## Need convergent solution...

Dear, I am facing the problem for solvin the attached file. Solution obtained for L=1 successfully but i need the solution for large value of L e.g., L =10. Please find the attachement and fix the problem. I am waiting positive response. Thanks in advance.

Help.mw