$32\mathrm{.}6$ In Problem $32\mathrm{.}3,$ Professor Nightsoil's utility function, is $U_N(B_N,P_N)=B_N+4P_N^{\frac{1}{2}}$ and Dean Interface's utility function is $U_{\text{I}}(B_{\text{I}},P_{\text{I}})=B_{\text{I}}+2P_{\text{I}}^{\frac{1}{2}}.$ If Nightsoil's initial endowment is $7$ bromides and $15$ platitudes and if Interface's initial endowment is $7$ bromides and $25$ platitudes, then at any Pareto efficient allocation where both persons consume positive amounts of both goods, it must be that