$(25$ pts$.)$ A company is considering opening a warehouse 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 Table below.

$\backslash$table$[[$To$],[$From$,$Region $1,$Region $2,$Region $3],[$New York,$20,40,50],[$Los Angeles,$48,15,26],[$Chicago$,26,35,18],[$Atlanta$,24,50,35]]$

We want to meet the weekly demands at minimum cost, subject to the preceding information and the following restrictions:

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

At most two warehouses can be opened.

Formulate an IP $($integer program$)$ that can be used to minimize the weekly costs of meeting demand.