the question gives the utility of two agents and their endow

the question gives the utility of two agents and their endowments and asks for the pareto efficient allocation. i tried to solve using the lagrangian. and just find that x2 of agent 1 is 81.9 or 122.1 and nothing about agent 2.
how can i solve the problem?

x 1x2 e\'s(100,0) ?2 ag (21x,-100-X2)\' O = 10000-204 x + (x BC fo X2-204 ± | 2042-40000 2.

Solution

You can find the solution to agent 2 by maximizing the utility unction of agent 2 subject to utility function of agent 1.

Solve in the same manner just maximize u2 now. You will get a value for agent 2.