A company wants to expand its market by building two new offices to cover four markets. The company wants to minimize the cost of building the two new offices while all four markets are covered. The regions that can be covered by each office are indicated by a $1$ in the following table.

New office cites

Markets

$1$

$2$

$3$

$4$

A

$1$

$1$

B

$1$

$1$

$1$

C

$1$

$1$

$1$

D

$1$

$1$

Cost

$200$

$120$

$190$

$250$