Finding Maximum out of a symbolic list given some constraints

Questions
1

Hey Guys,

I have solution in the form of a list as follows,

Max[0. + Abs[-1.75447*10^6 - 0.184261 T] +
  Abs[-2868.55 + a + 0.276392 T],
0. + 2 Abs[-1.75447*10^6 - 0.184261 T] +
  Abs[3.50321*10^6 + 0.368522 T],
0. + 2 Abs[-31999.5 - 0.221113 T] + Abs[-86832. - 0.1 T] +
  Abs[86832. + 0.1 T] + Abs[58261.9 + 0.442226 T],
0. + Abs[-1.75447*10^6 - 0.184261 T] + Abs[-2868.55 + d + 0.66334 T],
  0. + Abs[-31999.5 - 0.221113 T] + 2 Abs[86832. + 0.1 T] +
  Abs[-2868.55 + b + 0.773896 T],
0. + Abs[-31999.5 - 0.221113 T] + 2 Abs[-86832. - 0.1 T] +
  Abs[-2868.55 + e + 0.906564 T],
0. + 2 Abs[157081. - 0.180903 T] + Abs[-86832. - 0.1 T] +
  Abs[86832. + 0.1 T] + Abs[628326. + 1.44722 T],
0. + Abs[157081. - 0.180903 T] + Abs[-86832. - 0.1 T] +
  Abs[86832. + 0.1 T] + Abs[-5.47701*10^-13 + c + 5.60799 T],
0. + Abs[157081. - 0.180903 T] + Abs[-86832. - 0.1 T] +
  Abs[86832. + 0.1 T] + Abs[-5.47701*10^-13 + f + 5.78889 T]]

but I am unable to find the Max out of this list. Actually this list have some undefined variables. What if I want to check that which solution of this list is Maximum of all according to the following constraints over the variables which are used in the solution list.

/.{a > 2631708, b > 111998, c > 2434762, d > 6316099, e > 131197, f > 2513302}]

Regards,

2

Please clarify the question. If you take just 2 elements from your list, I mean

0. + Abs[-1.75447*10^6 - 0.184261 T] + Abs[-2868.55 + a + 0.276392 T]

and

0. + 2 Abs[-31999.5 - 0.221113 T] + Abs[-86832. - 0.1 T] +   Abs[86832. + 0.1 T] + Abs[58261.9 + 0.442226 T]

(do you really need zeros here?) and generate a 3D plot of these two planes, say, for a from 2631708 up to 10^7 and for T from 0 to 2000

Plot3D[{Abs[-1.75447`*^6 - 0.184261` T] +
   Abs[-2868.55` + a + 0.276392` T],
  2 Abs[-1.75447`*^6 - 0.184261` T] +
   Abs[3.50321`*^6 + 0.368522` T]}, {a, 2631708, 10^7}, {T, 0, 2000}]

then you may see that for some region the first function has bigger values and the second one has bigger values for the other domains

3

yes zeros can be ignored, but I cannot ignore other values by just considering just two of them. I have to find one Maximum solution out of available 9 solutions please go through my previous post I think I made it very clear.