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 y₁ = 1 if a plant is constructed in Detroit; 0 if not y₂ = 1 if a plant is constructed in Toledo; 0 if not y₂ = 1 if a plant is constructed in Denver; 0 if not y = 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. *,, = 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 example is as follows. Min 5x11 + 2x12 + 3×13 +421 + 3x22 + 4x23 +9x31 +7x32 + 5×33 +10x41 + 4x42 +2x43 +8x1 + 4x2 + 3x3 + 175y + 300у2 + 375y3 + 5004 s.t. *11 +×12 +×13 s10y Detroit capacity ×21 + x22 + x23 20y, Toledo capacity X31 + x32 + X33 ≤ 30y₁ Denver capacity X41 42 43 ≤40y Kansas City capacity X51 +52 + x53 < 30 St. Louis capacity Boston demand x12x22x32 + x42 + x2 = 20 Atlanta demand x13x23x3 + x43x53 = 20 Houston demand x,, ≥ 0 for all i and j; y₁₂ Yar Y₁ = 0, 1 (a) Modify the original formulation to account for the policy restriction that there must be one plant either Detroit or Toledo, but not both. new constraint (V1 V2 V3 V4)= Place x, in row i column j. 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 (V1 V2 V3 V4)= Place x, in row i column j.