MATH DER Q6 (please answer tis question not other questions that has nothing to do with this)

The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to determine which cities Martin-Beck should construct a plant in. Let 1 if a plant is constructed in Detroit; 0 if not Y = 1 if a plant is constructed in Toledo; 0 if not Y3 = 1 if a plant is constructed in Denver; 0 if not Y4 = 1 if a plant is constructed in Kansas City; 0 if not. The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem. x = the units shipped in thousands from plant i to distribution center j i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and j= 1 (Boston), 2 (Atlanta), 3 (Houston) The complete model for the Martin-Beck distribution system design problem is as follows. Min 5x11 + 2x12 + 3x13+4x21 + 3x22 + 4x23 +9X31 +7X32 + 5x33 + 10x41 + 442 + 2x43 + 8x51 + 4x52 + 3x53 +175y + 300%2+375y3 + 500/4 5.t. Detroit capacity X11X12X13 X21 + X22 + x23 10/ 201 30y3 Toledo capacity Denver capacity 40/4 Kansas City capacity 30 X31X32X33 X41X42X43 X51+x52 + X53 X11 X21 + X31 + X41 + X51 = 30 *12+ X22 + 32 + x42 + x52= 20 St. Louis capacity Boston demand Atlanta demand X13 + x23 + x33 + x43 + X53= 20 Houston demand xij0 for all / and j; V V2 V3 V4 = 0, 1 (a) Modify the original formulation to account for the policy restriction that there must be one plant in either Detroit or Toledo, but not both. new constraint (V V2 V3 V4) = Place x in row / column /. value= (b) Modify the original formulation to account for the policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. new constraint (Y V2 V3 V) ( Place x in row / column j. 00000 00000 value=