The State of Texas frequently does tax audits of companies doing business in Texas. These companies often have headquarters located outside the state, 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. Texas 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