For the revised problem statement:
DCp1Total = 3/5;
DCp2Total = 3/10;
DCpA0 = 1/2;
DCpB0 = 2/5;
eq[1] = DCp1Total == WA1*DCpA0 + WB1*DCpB0 // Simplify;
eq[2] = DCp2Total == WA2*DCpA0 + WB2*DCpB0 // Simplify;
eq[3] = WA1 + WB1 == 1;
eq[4] = WA2 + WB2 == 1;
min = Minimize[Total[(Subtract @@@ (eq /@ Range[4]))^2], {WA1, WA2, WB1, WB2}]
(* {0, {WA1 -> 2, WA2 -> -1, WB1 -> -1, WB2 -> 2}} *)
Or,
sol = Solve[eq /@ Range[4], {WA1, WA2, WB1, WB2}]
(* {{WA1 -> 2, WA2 -> -1, WB1 -> -1, WB2 -> 2}} *)
EDIT: To restrict variables to positive values, add constraints.
min2 = Minimize[{Total[(Subtract @@@ (eq /@ Range[4]))^2],
Thread[{WA1, WA2, WB1, WB2} > 0]} // Flatten, {WA1, WA2, WB1, WB2}]
(* Minimize::wksol: Warning: there is no minimum in the region in which the
objective function is defined and the constraints are satisfied; returning a
result on the boundary. *)
(* {43/442, {WA1 -> 31/26, WA2 -> 0, WB1 -> 0, WB2 -> 13/17}} *)
Since the minimum is not zero, there is no solution and you can only minimize the objective.
DCp1_total
toDCp1Total
andDCp2_total
toDCp2Total
._
is a reserved character. Change the=
to==
and then give your equations toSolve
. I don't think your system of equations has a solution. But you can always check. $\endgroup$