(a) Formulate a linear programming model of the problem. (Express your answers using Xij, where each X;; is either 0 or 1 for the arc from node i to node j.) Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows Node 7 Flows For all x = 0, 1. (b) Find the shortest route from node 1 to node 7 in the network shown. (Enter your answers as a comma-separated list.) path= 1, ,7
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- Consider the following transshipment network for finding the shortest route from node 1 to node 7. Min s.t. Node 1 Flows X12 +*13 Node 3 Flows Node 4 Flows Node 5 Flows 18 Node 6 Flows Node 7 Flows w +x14 X Node 2 Flows -x12 - x32-x52 + x23+x25 = 0 3 4 (a) Formulate a linear programming model of the problem. (Express your answers using Xij, where each x¡¡ is either 0 or 1 for the arc from node i to node j.) 5 4 3 6 3 6 79-43. Northwest University is in the process of complet-ing a computer bus network that will connect com-puter facilities throughout the university. The prime objective is to string a main cable from one endof the campus to the other (nodes 1–25) throughunderground conduits. These conduits are shownin the network below; the distance between them isin hundreds of feet. Fortunately, these undergroundconduits have remaining capacity through which thebus cable can be placed.(a) Given the network for this problem, how long (inhundreds of feet) is the shortest route from node1 to node 25?(b) In addition to the computer bus network, a newphone system is also being planned. The phonesystem would use the same underground conduits. If the phone system were installed, the follow-ing paths along the conduit would be at capacity and would not be available for the computer busnetwork: 6–11, 7–12, and 17–20. What changes(if any) would you have to make to the pathused for the computer bus if the phone…BETTER PRODUCTS COMPANY has decided to start manufacturing four new products in three plants that currently have excess production capacity. The products require comparable production effort per unit, so the available production capacity in the plants is measured by the number of units of any product that can be manufactured per day. a)Formulate this problem as a transportation problem by constructing the appropriate parameter table. I already have an optimal solution (it's from the book). (I dont understand)-------------------------------------------------------------------------OPTIMAL SOLUTION:It has basic variables (assignments) X₁₂ = 30, X₁₃ = 30, X₁₅ = 15, X₂₄ = 15, X₂₅ = 60, X₃₁ = 20 and X₃₄ = 25, so that: Plant 1 produces all of products 2 and 3.Plant 2 produces 37.5% of product 4.Plant 3 produces 62.5% of product 4 and all of product 1. The total cost of Z = $3 260 per day.-------------------------------------------------------------------------Instructions:Please explain this…
- BETTER PRODUCTS COMPANY has decided to start manufacturing four new products in three plants that currently have excess production capacity. The products require comparable production effort per unit, so the available production capacity in the plants is measured by the number of units of any product that can be manufactured per day. a)Formulate this problem as a transportation problem by constructing the appropriate parameter table. I already have an optimal solution (it's from the book). (I dont understand)-------------------------------------------------------------------------OPTIMAL SOLUTION:It has basic variables (assignments) X₁₂ = 30, X₁₃ = 30, X₁₅ = 15, X₂₄ = 15, X₂₅ = 60, X₃₁ = 20 and X₃₄ = 25, so that: Plant 1 produces all of products 2 and 3.Plant 2 produces 37.5% of product 4.Plant 3 produces 62.5% of product 4 and all of product 1. The total cost of Z = $3 260 per day.-------------------------------------------------------------------------Instructions:Please explain this…A company with a network of 10 pipelines transports mango juice according to the details shown in Table 1. Determine the maximum flow per hour. 1. Table/Jadual 1 Сарacity Node Node (m3/h) 140 100 120 100 120 80 110 100 100 100 Reverse Capacity |(m³/h) 60 20 40 40 40 20 30 40 60 60 Start End Pipeline 1 2 3 4 1 1 1 2 3 4 6 6 7 3 7 7 8 8 10Travelling Salesman Problem (TSP); Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance? Distances W 1 2 3 4 in miles 18 57 27 50 18 0 65 29 61 57 65 0 36 99 3 27 29 36 0 76 4 50 61 99 76 Route=W-1-3-2-4, Distance=182 miles Route=W-3-1-2-4-W, Distance=270 miles Route = W-3-1-2-4, Distance=220 miles Route=W-1-3-2-4-W, Distance=232 miles Route=W-1-3-4-2, Distance=272 miles 1, 2.
- LM.91 XYZ Company is rethinking the way it ships to its 74 customers in another city 222 miles away. Current Shipping/Delivery Method They currently hire an LTL (less-than-truckload) carrier to pick up and deliver these shipments. Each customer order shipped via LTL carrier costs $126. Alternate Shipping/Delivery Method A 3PL (third-party logistics provider) has approached XYZ Company and suggested that they make full truckload (TL) shipments from their facility to the 3PL's warehouse in the customers' city. The 3PL would then break the bulk shipment (TL or truckload shipment) into individual customer orders to be shipped locally by an LTL carrier. The relative data for this alternate shipping method are as follows: • Full TL shipment cost (222 miles) = $740 Average weight per customer order = 500 Ibs. • Warehouse break-bulk fee (per 100 lbs., a.k.a. per "hundred weight") = $13 • Local LTL delivery fee (per customer order) = $38 What is the total cost of delivering to all customers via…A truck driver has to deliver a load of lumber to oneof two construction sites, which are, respectively, 27 and 33 miles from the lumberyard, but he has misplaced theorder telling him where the load of lumber should go. The two construction sites are 12 miles apart, and, to compli-cate matters, the telephone at the lumberyard is out of order. Where should he go first if he wants to minimizethe distance he can expect to drive and he feels that(a) the odds are 5 to 1 that the lumber should go to theconstruction site that is 33 miles from the lumberyard;(b) the odds are 2 to 1 that the lumber should go to theconstruction site that is 33 miles from the lumberyard;(c) the odds are 3 to 1 that the lumber should go to theconstruction site that is 33 milesA bank has its head office in the financial district in the middle ofa city. A bank has six branches, three in the north of the city and threein the south all 5 km from the centre and spaced 3 km apart. The bankwishes to link all its branches via private leased lines but mustdecide between providing an individual line to each branch via anumber of inter-branch links and a smaller number of multiplexed linesto the centre. If a modem costs £100, a multiplexer/demultiplexercosts £200 and leased lines cost £100 per km per year to rent, suggesta design that will yield the most cost effective solution if theinstallation is to remain in operation for four years. 1st option is - link all branches by providing individual line to each branch via a number of inter branch links to the centre. 2nd option is - link all branches by providing smaller number of multiplexed lines to the centre Please calculate both options and choose the most cost effective solution for four years?
- 9-39. Grey Construction would like to determine the leastexpensive way of connecting houses it is buildingwith cable TV. It has identified 11 possible branchesor routes that could be used to connect the houses.The cost in hundreds of dollars and the branches aresummarized in the following table. (b) After reviewing cable and installation costs,Grey Construction would like to alter the costsfor installing cable TV between its houses.The first branches need to be changed. Thechanges are summarized in the followingtable. What is the impact on total costs?eBook Problem 10-31 A long-distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over that branch of the network. To keep up with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a oty located at node 7. 3 Maximum number of messages -Q.) Given the following network, with the indicated flow capacities along each branch, determine the maximum flow from source rode 1 to destination node 6 and the flow along each branch: 15 12 20 0 14 11