Delta company has 3 plants with 4 distribution centers across the state. The company has 5 wholesalers in its network that gets its products through the distribution centers. The number of decision variables in a linear program to calculate its minimum shipping cost is: Please do fast ASAP
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- A firm has established a distribution network for the supply of a raw material critical to itsmanufacturing. Currently there are two origins for this material, which must be shipped to threemanufacturing plants. The current network has the following characteristics: COSTS PLANT 1 PLANT 2 PLANT 3 SUPPLY Raw Material source 1 $6 $8 $9 400 Raw Material source 2 $4 $7 $3 600 Demand 500 500 500 Supply < Demand The firm has identified two potential sites for a third raw material source; these are identified asCandidate A and Candidate B. From A, the costs to ship would be $9 to Plant 1, $10 to Plant 2,and $12 to Plant 3. From B, these costs would be $11, $14, and $8. The new source, wherever itis located, will have a capacity of 500 units. Solve with the transportation method. Which siteshould be selected?DM Office Products (DMOP) is a wholesale supplier of office products with one facility in Pennsylvania. They have decided to build a new distribution warehouse in the state of New York to help serve the growing demand in that market. They have four major customers located in Buffalo, Syracuse, Albany, and New York City. Though New York City is the largest market, it also has the greatest competition and DMOP is not a major player there. When DMOP ships an order to a customer they use their own small fleet of two trucks to deliver, so the cost of delivery is essentially the same for a full or partially full truck. The expected number of annual shipments to each city and their coordinates on an x, y grid is shown in the following table. CITY Buffalo Syracuse Albany New York x-COORDINATES 370 1,465 2,345 2,320 y-COORDINATES 895 945 675 70 NUMBER OF SHIPMENTS 96 100 140 80 Use the centroid method to recommend a location for the new warehouse for DMOP (Round your answers to 1 decimal…Given the following transportation matrix where the numbers in the cells represent cost of transporting 1 unit from a specific source to a specific destination, determine the initial solution using the 3 methods and determine the optimum solution by using the initial solution with the lowest value of Z. 3 4 5 6 35 Dummy Supply From/To 1 40 M M 100 60 45 M M 200 12 20 M 300 4 15 10 30 300 5 M M 15 300 Demand 300 | 300 300 150 150 1,200
- ABC pharmaceutical Company has four factories that ship supplies to four warehouses. The company’s management hires you as a consultant to determine a minimum-cost shipping plan for its monthly output to the warehouses. Factory capacities, warehouse demands, and shipping cost per box are shown below. Factory Supply or capacity (boxes) Warehouse Demand (boxes) Richmond 60 Chicago 100 Santa Fe 80 Jacksonville 90 Austin 120 Huntville 50 Vacaville 90 Fresno 70 Shipping Costs per box (In Dollars) From To Chicago To Jacksonville To Huntsville To Fresno Richmond 35 35 46 60 Santa Fe 65 40 35 25 Austin 50 50 80 90 Vacaville 40 40 66 75 Draw a diagram by showing factories, warehouses, and connecting arcs. Define variables, write the objective function and constraints.Suppliers A, B, and C supply components to three plants -- F, G, and H via two transshipment facilities -- T1 and T2. It costs $4 to ship from T1 regardless of final destination and $3 to ship to T2 regardless of supplier. Shipping to T1 from A, B, and C costs $3, $4, and $5, respectively, and shipping from T2 to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. The Logistics Manager has come to you for help. Answer the following question: Which of these is not an element of the objective function? Group of answer choices 4D-T1 600T1 9T2-G 3C-T2 Plz do fast asapPrescott Industries transports sand and stone extracted from its open-pit mines located in Odessa and Bryan to its concrete block manufacturing facilities in Abilene, Tyler and San Angelo. For the capacities, locations, and shipment costs per truckload shown in the tableau below, determine the shipping pattern that will minimize transportation costs. What are the estimated transportation costs associated with this optimal allocation pattern? Source Odessa Bryan Demand Source Odessa Bryan Abilene $90 Demand $45 4,500 Abilene $90 $45 Destination Tyler 4,500 $25 $90 Fill in the tableau below by indicating the optimal number of shipments from a source to a destination in each cell. (Enter your responses as whole numbers. A response of "0" is equivalent to no shipments being planned.) The corresponding optimal total cost is $ 8,400 Destination Tyler $25 $90 San Angelo $75 8,400 $50 6,100 San Angelo $75 $50 Capacity 6,100 8,400 10,600 Capacity 8,400 10,600 (Enter your response as a whole…
- The Thor International Company operates four factories that ship products to five warehouses. The shipping costs, requirements, and capacities are shown in the tableau below. Use the transportation method to find the shipping schedule that minimizes shipping cost. Factory Shipping Cost per Case to each Warehouse Capacity W1 W2 W3 W4 W5 Dummy F1 $4 $5 $4 $3 $6 $0 50,000 F2 $3 $4 $4 $5 $7 $0 80,000 F3 $3 $4 $5 $3 $5 $0 90,000 F4 $4 $6 $5 $6 $3 $0 40,000…The Thor International Company operates four factories that ship products to five warehouses. The shipping costs, requirements, and capacities are shown in the tableau below. Use the transportation method to find the shipping schedule that minimizes shipping cost. Shipping Cost per Case to each Warehouse W2 Factory Сарacity W1 W3 W4 W5 Dummy $5 $5 $4 $7 $0 F1 60,000 $4 $5 $4 $6 $8 $0 F2 80,000 $6 $5 $7 $4 $5 $0 F3 80,000 $5 $9 $6 $7 $4 $0 F4 40,000 Demand 45,000 40,000 30,000 35,000 50,000 60,000 260,000 The minimum shipping cost is S | (Enter your response as a whole number.)A company has three existing warehouses to which it will ship furniture from a new factory whose location must be decided. The factory will receive raw materials from its wood supplier and fabric supplier. The annual number of shipments, shipment costs and the location of the suppliers and warehouses are shown below Existing facilities Annual L to or from fact cost Coordinate location Wood supplier 120 10 (100, 400) Fabric supplier 200 10 (800,700) Ware h 1 61 10 (300, 600) Ware h 2 40 10 (200, 100) Ware h 3 70 10 (600, 200) Using the median load answer the following questions –Where the factory should be located to minimize annual transportation cost –What will be the minimum annual transportation cost
- There are four factories producing a product that is needed in six destinations. In the table on the left there are the number of products available at the factories, their production costs. For the desinations the selling price of an item and the maximum needed quantity in each destination is given. In the framed boxes the transporation cost of one item from factory to destination are given. Find the number of items to shipTRANSPORTATION Given the following transportation matrix where the numbers in the cells represent cost of transporting 1 unit from a specific source to a specific destination, determine the initial solution using the 3 methods and determine the optimum solution by using the initial solution with the lowest value of Z. From/To 1 2 3 3 4 40 60 0 5 6 Dummy 35 M M 0 45 M M 12 20 M 4 15 0 10 30 5 M M 0 15 Demand 300 300 300 150 0 0 0 0 150 Supply 100 200 300 300 300 1,200Consider the transportation problem having the following parameter table: Source Demand 12 2 Destination 1 8 6 3 2 54 3 Supply 4 2 (a) Use the northwest corner rule to obtain an initial BF solution, and then solve this problem manually by the transportation simplex method. (Keep track of your time.) (b) Reformulate this problem as a general linear programming problem, and then solve it manually by the simplex method. Keep track of how long this takes you, and contrast it with the computation time for part (a).