A chain of home health care firms in Louisiana needsto locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scat-tered throughout the state, as detailed in the following table. Each site, except for Houma, will be visited three times each year by ateam of workers, who will drive from the central office to the site. Houma will be visited five times a year. Which coordinates rep-resent a good central location for this office? What other factors might influence the office location decision? Where would youplace this office? Explain. PXCITY MAP COORDINATESx yCovington 9.2 3.5Donaldsonville 7.3 2.5Houma 7.8 1.4Monroe 5.0 8.4Natchitoches 2.8 6.5New Iberia 5.5 2.4Opelousas 5.0 3.6Ruston 3.8 8.5

Cargo Loading. You are in charge of loading cargo ships for International Cargo Company (ICC) at a major East Coast port. You have been asked to prepare a loading plan for an ICC freighter bound for Africa. An agricultural commodities dealer would like to transport the following products aboard this ship:Commodity    Tons Available    Volume per Ton (cu.ft.)    Profit per Ton ($)1    4,000    40    702    3,000    25    503    2,000    60    604    1,000    50    80You can elect to load any or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions: Cargo Hold    Weight Capacity (tons)    Volume Capacity (cu.ft.)Forward    3,000    100,000Center    5,000    150,000Rear    2,000    120,000More than one type of commodity can be placed in the same cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 10 percent of the weight in the rear cargo hold, and the center cargo hold…

Here is the initial tableau (by the NorthWest method) of a Min transportation problem. 1 2 3 Demand 19 Dual(v) 1 15 9 S1: 11 10 14 0 S2: 0 S3: B 0 B 3 N 15 Demanders 2 8 0 9 12 188 15 9 21 5 N 0 B 0 B 13 10 8 8 20 3 0 20 -4 N -6 N 0 B 17 7 5 4 0 0 1 -14 N -8 N 0 B Supply Dual(u) 0 (188 188 188 188 Using the Loop method fill in the values of the next tableau Each 2x2 matrix is the relevant square in the tableau. 9 (For grading convenience, in bottom right corner of each box use 1 for "B" and 0 for "N") 22 188 188 188 30 -4 2

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