A company is considering opening warehouses in four cities: New York, Los Angeles,

Chicago, and Atlanta. Each warehouse can ship $100$ units per week. The weekly fixed cost of

keeping each warehouse open is $$400$ for New York, $$500$ for Los Angeles, $$300$ for

Chicago, and $$150$ for Atlanta. Region $1$ of the country requires $80$ unites per week, region $2$

requires $70$ unites per week, region $3$ requires $40$ units per week. The costs $($including

production and shipping costs$)$ of sending one unit from a plant to a region are shown in the

table. we want to meet weekly demands at minimum cost, subject to the preceding

information and the following restrictions:

$1.$ If the New York warehouse is opened, then Los Angeles warehouse must be opened.

$2.$ At most two warehouses can be opened.

$3.$ Either the Atlanta or the Los Angeles warehouse must be opened.