What are the values of t1,t2,t3,t4, and t5 at the maximum of the following expression, in terms of parameters a1,a2,a3,a4,a5, and a6?

(t1+t3+t5)*(t1a1)*(t2a2)*(t3a3)*(t4a4)*(t5a5)*((1-t1-t2-t3-t4-t5)a6)



The variables and parameters are subject to the following constraints:

0 ≤ t1 ≤ 1
0 ≤ t2 ≤ 1
0 ≤ t3 ≤ 1
0 ≤ t4 ≤ 1
0 ≤ t5 ≤ 1
0 ≤ t1 + t2 + t3 + t4 + t5 ≤ 1

a1 > 0
a2 > 0
a3 > 0
a4 > 0
a5 > 0
a6 > 0