Example $7$: $($Winston$,$ pp$.503)$

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

Atlanta. Each warehouse can ship $100$ units per week. The weekly fixed cost of keeping each 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 $4$

requires $40$ units per week. The costs $($including production and shipping cost$)$ of sending one unit from

a plant to a region are shown in the following table. We want 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 warehouses can be opened.

Either the Atlanata or the Los Angeles warehouses must be opened.

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