Answer the next two questions based on the case given below: 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 Houston and Tulsa, and consider new plants in Santa Fe, Detroit, and Portland. Finished control panels are to be shipped to Seattle, Denver, and Kansas City. Pertinent information is given in the table. 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 to minimize construction plus shipping costs. Let xij= the number of panels shipped from source i to destination j yi=1ifplantiisbuilt,=0otherwise(i=3,4,5) The constraint for demand at Seattle is given as: x11+x21+x31+x41+x51=30,000x11+x21+x31+x41+x51>=30,000bothx11+x21+x31+x41+x51>=30,000andx11+x21+x31+x41+x51=30,000wouldbecorrect.x11+x21+x31+x41+x51=30,000y1 Answer the next two questions based on the case given below: 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 Houston and Tulsa, and consider new plants in Santa Fe, Detroit, and Portland. Finished control panels are to be shipped to Seattle, Denver, and Kansas City. Pertinent information is given in the table. 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 to minimize construction plus shipping costs. Let xij= the number of panels shipped from source i to destination j yi=1 if plant i is built, =0 otherwise (i=3,4,5) The optimal objective function value would not exceed $1,200,000. We can't know without solving the problem. False True