## Cournot Model Optimisation Problem

I am unable to find a solution to firm 2's best response for part (iv) of the following:

http://i.imgur.com/P1XKp2X.png

The best response functions were found in part (i) by maximising each firm's individual profit functions (where profit = revenue - cost) ie.

firm 1 : (80 - (q1 +q2))q1 - 10q1

firm 2: (80 - (q1 + q2))q2 - 6q2

Taking the partial derivative of each of these results in best response functions:
q1 = 35 - 0.5q2 & q2 = 37 - 0.5q1

I have attempted part (iv) by trying to maximise (80 - q1 + q2)q2 - 6q2 - (40 - (0.5q1 +.05q2))0.5q1 - 5q1 = 0

80q2 - q1q2 - q2^2 - 6q2 - 20q1 - 0.25q1^2 - 0.25q1q2 - 5q1 = 0

74q2 - q1q2 - q2^2 - 25q1 - 0.25q1^2 - 0.25q1q2 = 0

74q2 - 1.25q1q2 - q2^2 - 25q1 - 0.25q1^2 = 0

taking the partial derivative with respect to q2 -

74 - 1.25q1 = 2q2

37 - 0.625q1 = q2

I know this is the wrong answer. The lecturer posted this solution but I can't make sense of how she did it:

http://i.imgur.com/p0jmURO.png

Any help would be really appreciated.