A beer distributor needs to plan how to make deliveries from its warehouse (node 1) to a supermarket (node 7), as shown in the network below. 1 3 3 11 6 3 5 6 3/ 3 4 7 +4x47 +9x56 +3x67 Develop the LP formulation for finding the shortest route from the warehouse to the supermarket. (Let X;; represent the flow from node i to node j.) Min 3x12 + 3x15 + 11x16 + 6x23 +5x34 + 3x46¯ X
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- 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…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 7
- Travelling 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, 2.9-43. 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…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 -
- #63 (use the Stepping Stone Method to find an optimal solution for graph "a")Maximal Flow a. Write the linear program for this problem. b. Create a spreadsheet model to find the maximal flow from node 1 to 6LM.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 milesConsider the transportation problem having the following data: c) write the algebraic formulation of this problem.please do it in excel 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. Note:One image is of the data and the other image is option 1 to solve the exercise.