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TABLE 11 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 11. 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 the 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. Formulate an IP that can be used to minimize the weekly costs of meeting demand. 12 A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each a) Fallow' the following stepe to formulate the jroblesm as shownt belos: Step-1: Decide the decision variables: In current problem, the decinions are, 1) Should a watrhouse be openes an caty b6. 2) Hew many units to thep from warehoose ito city j Let the decision variables be: y1={1ifthewarebouseincityiisselectedforopeningthewarchose0otherwise}. x1= Number of units stppliedfroen location felocation f Step-2: Formulate the objective function: the shipping cost, Write a mathematical eqaation to regresent thas, as absan belon: =400y3+500yz+300yz+400y4+20x2+40x2+40x2+45xz+15xz +26xy+26x11+35xn+18x2+34xe+50xet+34xe Step-3: Setep constraints as shown belewt Shipping capacity ceastraints: x11+x2+x2y100y1x21+x21+x21100y2x11+x12+x2j100y1x2i+xeq+xe100y1 Demand constraint: x11+x21+x11+xe1=50x12+x2+x12+xed=70x11+x23+x22+xe=40 Constraint: If the New York wareheese is opened, then the Les Angules warebeuse must be opened. .y: Convtraiet: At most three warebeeses, can be opened. y1+y2+y1+y43 Contraint Either the Atlanta or the Les Angrles warehouse mast be opened. y2+y4=1