Amazon Inc. 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 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 cost $($including production and shipping costs$)$ of sending one unit from a

warehouse to a region are shown in the following table.

Region $1$ Region $2$ Region $3$

New York $204050$

Los Angeles $481526$

Chicago $263518$

Atlanta $245035$

Amazon wants to meet 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 warehouse can be opened.

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

Formulate an IP to help Amazon Inc. decide what warehouses to open. Clearly state your decision variables