Recall the split the dollar example discussed in class. In that example there are two individuals (A and B) and the set of possible allocations is

X = {(xA;xB) : xA > 0, xB > 0, xA +xB < 100}

Consider the following variation. The only difference is that now when two agents agree on (50, 50), each gets 20 as a bonus. What are the Pareto optimal allocations? (An allocation specifies how much each agent ultimately gets.) What the bonus associated with (50, 50) is 60 each?