A construction company has been hired to build a custom home. The builder estimates the probabilities of potential profit $($or loss$)$ as shown in the table below.

$\backslash$table$[[$Profit$/$Loss$,$Probability$],[$$$100,000,0\mathrm{.}20],[$$$60,000,0\mathrm{.}20],[$$$30,000,0\mathrm{.}30],[0,0\mathrm{.}20],[-$$$20,000,0\mathrm{.}08],[-$$$40,000,0\mathrm{.}02]]$

What is the profit expectation for the company?

$$34,600$