$(20$ Points$)$ The IRS frequently does tax audits of companies doing business in the USA. These companies often have headquarters located all over the states, so auditors must be sent to out$-$of$-$state locations. Each year, auditors must make $500$ trips to cities in the Northeast, $400$ trips to cities in the Midwest, $300$ trips to cities in the West, and $400$ trips to cities in the South. The IRS is considering basing auditors in Chicago, New York, Atlanta, and Los Angeles. The annual cost of basing auditors in any city is $$100,000.$

The cost of sending an auditor to these cities is given below:

$\backslash$table$[[,$Auditor Cost $($$$)$