Question: How to minimize cost function

Dear Sir
Can you please help me to minimize the following cost function with maple 10.I want that " t and T must be greater than zero(not equal to zero) , t < T  and C > 0." I tried a lot but I am not getting the values of t and T as mentioned above " ". Also why  the solution obtained by the 2 methods below is different  ? Which one of them is correct ?

Priyaasha

C:=(a*c1*(6*beta*t^2-alpha*beta*t^4+alpha*T^4-2*alpha*t*T^3+2*alpha*t^3*T+6*T^2-12*t*T)/12+b*c1*(20*beta*t^3-3*alpha*beta*t^5+40*T^3-60*t*T^2+10*alpha*t^3*T^2+8*alpha*T^5-15*alpha*t*T^4)/120+a*c3*(beta*t-T)+b*c3*(beta*t^2-T^2)/2+alpha1*beta*(a^(2-gamma)-(a+b*t)^(2-gamma))/(b*(gamma-2)))/T;

C1:=subs(a=20,b=12,c1=4,c3=8,alpha=0.01,beta=4,alpha1=16,gamma=1.2,C);

Optimization:-Minimize(C1,assume=nonnegative);

C=−160.998836576159988 , t = 0 , T = 0.249548625906505560

Cdt:=diff(C,t);

CdT:=diff(C,T);

X1:=subs(a=20,b=12,c1=4,c3=8,alpha=0.01,beta=4,alpha1=16,gamma=1.2,Cdt):

X2:=subs(a=20,b=12,c1=4,c3=8,alpha=0.01,beta=4,alpha1=16,gamma=1.2,CdT):

X3:=fsolve({X1,X2},{t,T})assuming t::positive,T::positive;

T = −2.499483777 , t = −1.266595506

C2:=eval(C1,[t=−1.266595506,T= −2.499483777]);

Also i am not getting the value of C for t =−1.266595506, T = −2.499483777