Hansen Controls has been awarded a contract for a large number of control panels. To meet this demand, it will use its existing plants in San Diego and Houston, and consider new plants in Tulsa, St. Louis, and Portland. Finished control panels are to be shipped to Seattle, Denver, and Kansas City. Pertinent information is given in the table. Shipping Cost to Destination: Capacity Seattle 1 Denver 2 Kansas City 3 1- San Diego ---- 5 7 8 8,000 2- Houston ---- 8 10 6 12,000 3- Tulsa 350,000 12 6 3 10,000 4- St. Louis 400,000 12 4 2 7,000 5- Portland 480,000 4 10 11 9,000 Demand 11,000 8,000 7,000 We develop a transportation model as an LP that includes provisions for the fixed costs (construction costs in this case) for the three new plants. The solution of this model would reveal which plants to build and the optimal shipping schedule. Let x = the number of panels shipped from source i to destination j y = 1 if plant i is built, = 0 otherwise (i = 3, 4, 5) The constraint for supply from St. Louis is given as: None of the others. Correct! x41 + x42 + x43 <= 7,000 12x41 + 4x42 + 2x43 <= 7,000 y4 12x41 + 4x42 + 2x43 <= 7,000 x14 + x24 + x34 <= 7,000 y4