A minimum-cost flow problem has 8 supply nodes, O transshipment nodes, and 7 demand nodes. If each supply node can ship to every demand node, how many arcs will be included in the model? Number of arcs

Given the following network, with the indicated flow capacities of each branch, determine the maximum flow from source node 1 to destination node 6 and the flow along each branch:

(1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). B C 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route B 1 2 3 4 A 10 11 9 14 Step 1b: Column subtraction. Truck / Route 1 2 3 4 A 10-6=4 = = = = = B = с = C Step 2: Testing for optimal solution (show your lines covering the zero entries). What is the minimum number of lines required to cover all zeros? D 8 14 10 13 D = = D =

Bindley Corporation has a one-year contract to supply motors for all washing machines produced by Rinso Ltd. Rinso manufactures the washers at four locations around the country. New York City, Fort Worth, San Diego, and Minneapolis. Plans call for the following numbers of washing machines to be produced at each location: New York City Fort Worth San Diego Minneapolis Bindley has three plants that can produce the motors. The plants and production capacities are Boulder Macon Gary Due to varying production and transportation costs, the profit Bindley earns on each 1,000 units depends on where they were produced and where they were shipped. The following table gives the accounting department estimates of the dollar profit per unit. (Shipment will be made in lots of 1,000.) Macon Gary PRODUCED AT NEW YORK CITY Boulder 12 From/To Boulder Macon Gary Requirements 75,000 45,000 60,000 50,000 100,000 145,000 65,000 Candidate Solution Boulder Macon Gary Total supplied Profit 24 11 Boulder Macon…

each of the other six areas of the plant. 5. The Burger Doodle restaurant franchises in Los Angeles are supplied from a central warehouse in Inglewood. The location of the warehouse and its proximity, in minutes of travel time, to the franchises are shown in the following network: San Fernando Valley Burbank Pomona 28 25 36 35 18 asadena 29 50 45 41 Westwood 25 Downey 32 Anaheim 40 Inglewood 20 27 48 17 Long Beach 24 10 Huntington Beach Trucks supply each franchise on a daily basis. Determine the shortest route from the warehouse at Inglewood to each of the nine franchises.

Sean Willems has evaluated the vendors in Table S11.3 as well as F ricker V-Tech, the vendor in Problem( Referring to Problem S 11.1 2, Sean Willems, in additionto the two possible vendors evaluated in Table S11.3,has found a third possible vendor. He now wants to evaluate all three vendors using the weights in Table S 11 .3. He scores the third vendor, Fricker V-Tech, Ltd., as: Engineering Competence5, Process Capabili ty 5, Cost I, Quality 5, Performance to Schedule 4, and After-Sales Service I . Which vendor has the highest score? ),but the Quality Control Manager says that new da ta suggest thatSiemsen Systems, Inc.'s quality has deteriorated, a nd Siemsen should now score a 2 in the Quality category. Which of the three vendors now has the highest score?

like this fill the boxes

Required information The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec- tively. Each distribution center heeds to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Plant 1 2 3 1 1450 1750 1250 Distribution Center 3 1050 1250 1450 Obtain an optimal solution, and determine the total cost. Total Cost = $ 2 1950 2050 1850 The freight cost for each shipment is $100 plus 50 cents per mile. 4 1350 1650 1550

SOLVE USING EXCEL   Metal Fabricators, Inc. manufactures gas grill tanks, Model # 1420, for four original equipment manufacturers (OEMs). Demand is forecast to be as follows: Quarter 1 = 2,800 tanks, Quarter 2 = 3,400, Quarter 3 = 3,600, and Quarter 4 = 2,900. Due to a hedging program for sheet steel and increases in international tariffs, production cost per quarter vary as follows: Quarter 1 = $23.50 per tank, Quarter 2 = $28.00, Quarter 3 = $25.90, and Quarter 4 = $29.00. Due to production contracts with the OEMs, no shortages are allowed. Beginning inventory for Quarter 1 is 300 tanks. At the end of each quarter, inventory holding costs are $4.25 per tank. a. Formulate the problem as a linear programming model (see Supplement D).  b. Solve the model in (a) using Excel Solver.

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…