Mathematica:Having problem with my calculation(numerical)

[shafieza_garl]

What wrong with my calculation.the problem is from the attachment.
It keeps saying

NMinimize::nnum:The function value ...is not a number at {x1,x2}=...

given x0=0 and x3=5

 

[phyzguy]

Did you tell it what Y (capital Y) is? If so, you didn't tell us. NMinimize needs to know all of the values, it can't deal with variables.

 

[Bill Simpson]

In[1]:=x0=0;x3=5;
F[x_,y_]:=0.25`(4044.44444444445`-66.66666666666667`x+E^(-0.015x+0.015y)(-4044.44444444445`+66.66666666666667`y))^2;
H[x_,y_]:=Integrate[0.25`(E^(-0.015`t)(E^(0.015`t)(4044.44444444445`-66.66666666666667`t)+E^(0.015`y)(-4044.44444444445`+66.66666666666667`y)))^2,{t,x,y}];
NMinimize[{27+3*(F[x0,x1]+F[x1,x2]+F[x2,x3])+0.2*(H[x0,x1]+H[x1,x2]+H[x2,x3]),x0≤x1&&x1≤x2&&x2≤x3},{x1,x2}]

Out[4]={4.457054464608864`*10^8, {x1 -> 0.06690213249753463`, x2 -> 1.1629357790698616`}}

If I did not make an error typing this all back in again then I cannot explain what your problem is. But I believe you have larger problems than this. Quit kernel and restart

In[1]:=a=1/4;b=4044+4/9;c=66+2/3;d=15/1000;x0=0;x3=5;
F[x_,y_]:=a*(b-c*x+E^(-d*x+d*y)*(-b+c*y))^2;
H[x_,y_]:=Integrate[a*(E^(-d*t)*(E^(d*t)*(b-c*t)+ E^(a*y)*(-b+c*y)))^2,{t,x,y}];
NMinimize[{27+3*(F[x0,x1]+F[x1,x2]+F[x2,x3])+ 1/5*(H[x0,x1]+H[x1,x2]+H[x2,x3]),x0≤x1&&x1≤x2&&x2≤x3},{x1,x2}]

Out[4]={7.388367735069655`*10^6, {x1 -> 2.4650125379662637`, x2 -> 3.9306108222644514`}}

So very tiny changes in your coefficients give very different results.

I would suggest you spend a few days reading about the details of approximate and exact and machine precision mathematics as provided by Mathematica. Much of that is probably not what you would expect it to be.