# Im trying to solve a maximization problem: <munder> <mo movablelimits="true" form="pref

Im trying to solve a maximization problem:
$\underset{\mathbf{p}}{max}w\text{ln}\left(\sum _{i=1}^{I}{p}_{i}{a}_{i}\right)-\sum _{i=1}^{I}{p}_{i}{d}_{i},$
where ${p}_{i}\in \left\{0,1\right\}$ is binary variable and $\sum _{i=1}^{I}{p}_{i}=1$. I need to find optimal ${p}_{i}^{\ast }$, where
${\mathbf{p}}^{\ast }=\mathrm{arg}\underset{\mathbf{p}}{max}w\text{ln}\left(\sum _{i=1}^{I}{p}_{i}{a}_{i}\right)-\sum _{i=1}^{I}{p}_{i}{d}_{i}$
Is there any way to obtain the closed-form of ${p}_{i}^{\ast }$ as the function of $w$, ${a}_{i}$, and ${d}_{i}$?
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Giovanna Erickson
It is just ${p}_{i}=\left[i={i}^{\ast }\right]$, where ${i}^{\ast }=\mathrm{arg}\underset{i}{max}\left(w\mathrm{ln}{a}_{i}-{d}_{i}\right)$. The square brackets here are Iverson notation.