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 $80$ units per week, region $2$

requires $70$ units per week, and 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

following table.

The company wants to meet weekly demands at minimum cost subject to the following

restrictions:

If the NY warehouse is opened, then the Los Angeles warehouse must be opened.

At most two warehouses can be opened.

Either the Atlanta or the Los Angeles warehouse must be open.

Formulate an IP that can be used to minimize the weekly costs of meeting demand.