The question states that the sum of income of A and B is more than that of C and D combined. This means that A + B > C + D.

Next, the question states that the sum of income of A and C is the same as that of B and D combined. This means that A + C = B + D.

Finally, the question states that A earns half as much as the sum of the income of B and D. This means that A = (B + D)/2.

We need to find the highest income among A, B, C, and D.

By substituting the third equation in the second equation, we get (B + D)/2 + C = B + D.

Simplifying the equation, we get B + D + 2C = 2B + 2D.

Rearranging the terms, we get B + D – 2B – 2D = -2C.

Simplifying, we get -B – D = -2C.

Now, let`s consider the first equation (A + B > C + D).

By substituting the third equation in the first equation, we get (B + D)/2 + B > C + D.

Simpl