Answer the next two questions based on the case given below: Hansen Controls has been awarded a contract for a large manber 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, Derver, and Kansas City. Pertinent information is given in the table. Shipping Cost to Destination: Construction Kansas Sources Cost Seattle Denver City Capacity 1 2 3 1- Tulsa 10 6 5 15,000 2- Houston 8 7 6 25,000 3- Santa Fe 200,000 6 7 8 8,000 4- Detroit 300,000 12 5 11 10,000 5. Portland 400.000 3 8 10 14,000 Demand 30,000 20,000 10,000 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 to minimize construction plus shipping costs. Let Xu the number of panels shipped from source i to destination ; y=1 if plant i is built, = 0 otherwise (i = 3,4,5) The optimal objective function value would not exceed $1,200,000. O True We can't know without solving the problem. O False 8 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. Shipping Cost to Destination: Construction Kansas Sources Cost Seattle Denver City Capacity 1 2 3 1. Tulsa 10 6 5 15,000 2. Houston 7 6 25.000 3- Santa Fe 200,000 6 7 8,000 4- Detroit 300,000 12 5 10,000 5- Portland 400,000 3 8 10 14,000 Demand 30,000 20,000 10,000 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 to minimize construction plus shipping costs. Let x=the number of panels shipped from source i to destination y-l if plant i is built, -0 otherwise (i = 3,4,5) 8 The constraint for demand at Seattle is given as: o both x11 + x21 + x31 + x41 + x51 >= 30,000 and 11 + x21 + x31 + x41 + x51 - 30,000 would be correct. O X11 + x21 + x31 + x41 + x51 30,000 O x11 + x21 + x31 + x41 + x51 >= 30,000"y1 x11 + x21 +31 + x41+x51 > 30,000 O X11 + x21 + x31+x41+x51