Concept explainers
a)
Interpretation: convert the given problem into balanced problem by adding an appropriate row and column and find the optimal solution using solver.
Concept Introduction: one of the feasible solution is that the objective function ranges from maximum to minimum value depends upon the profit or loss of the cost problem is called optimal solution.. This kind of solution required by a company to solve the problem or to achieve the goal. This solutions that could maximize or minimize the profit or reduce the costs.
b)
Interpretation: Find the optimal solution using solver and inequality constraints.
Concept Introduction: For all kinds of optimization problem, there could be one or more than one optimal solutions and sometimes there is infinite number of optimal solutions are occurred. Optimal solution is the one type of feasible solution, which has the objective function reaches their goal.
c)
Interpretation: Compare the solutions in part a and part b and clarify the reason.
Concept Introduction: For all kinds of optimization problem, there could be one or more than one optimal solutions and sometimes there is infinite number of optimal solutions are occurred. Optimal solution is the one type of feasible solution, which has the objective function reaches their goal.
d)
Interpretation: Modify the model in Part b also resolve to find the optimal solution and clarify the objective value increased or decreased.
Concept Introduction: For all kinds of optimization problem, there could be one or more than one optimal solutions and sometimes there is infinite number of optimal solutions are occurred. Optimal solution is the one type of feasible solution, which has the objective function reaches their goal.
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Production and Operations Analysis, Seventh Edition
- 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 1550arrow_forwardFormulate a linear program using LP Model Formulation. Miguel hauls mangoes between Manila mango plantation and packing plants in Clark. Miguel’s schedule this week calls for 500 boxes with locations and costs as follows.arrow_forwardThe Arid Company makes canoe paddles to serve distribution centers in Worchester, Rochester, and Dorchester from existing plants in Battle Creek and Cherry Creek. Arid is considering locating a plant near the headwaters of Dee Creek. Annual capacity for each plant is shown in the right-hand column, while annual demand is shown in the bottom row of the tableau in Figure. Transportation costs per paddle are shown in the tableau in the small boxes. For example, the cost to ship one paddle from Battle Creek to Worchester is $4.37. The optimal allocations using the transportation method for location problems are also shown in Figure. For example, Battle Creek ships 12,000 units to Rochester. What are the estimated transportation costs associated with this allocation pattern?arrow_forward
- Maxie is leaving the Goucher Basketball jersey making business and is closing three of her factories. She would like to reassign all 235 of her best workers to Bianca's remaining factories. Closing Plant: No. of Workers to Transfer 1 60 2 105 3 70 Total: 235 However, demand for skilled labor in the Goucher basketball jersey making market has decreased. Bianca has three open plants that have openings, but not enough for all 235 employees looking to be transferred. The below table summarizes Bianca's current needs: Open Plant: No. of Open Positions A 45 B 90 C 35 Total: 170 Each worker who fills an open position on the assembly line will increase the number of Goucher basketball jerseys produced per day at each plant as shown in the following table: To: From: A B C 1 5 8 6 2 10 9 12 3 7 6 10 To maximize product output, how many workers should be assigned from Plant 1 to.. Plant A: Plant B: Plant C: from Plant 2 to.. Plant A: Plant B: Plant C: from Plant 3 to.. Plant A: Plant B: Plant C:…arrow_forwardConsider the following distribution system: Single product. Two plants, referred to as plant p1 and plant p2. Plant p2 has an annual capacity of 40,000 units. The two plants have the same production costs. • • Two existing warehouses, referred to as warehouse w1 and warehouse w2, have identical warehouse handling costs. • Three markets areas, c1, c2, and c3, with demands of 50,000, 100,000 and 50, 000, respectively, Table 1 provides distribution cost per unit. For instance, distributing one unit from plant p1 to warehouse w2 costs $5. Convert the following diagram into the table. No need for any calculation. Facility warehouse w1 W2 p1 2 3 p2 2 0 c1 3 5 c2 3 2 C3 4 3arrow_forwardThe 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.)arrow_forward
- Mount Isa Mines is one of the world’s great metal mines. Its main operations are at Mount Isa, in Queensland, Australia, where it mines adjacent deposits of copper and silver-lead-zinc ores. Production levels changes with world demand and prices, but in atypical year 7 million tonnes of ore are mined to give 150,000 tonnes of copper and lead (containing silver) and 200,000 tonnes of zinc. Mount Isa has serious transport problems. It produces huge quantities of ore in a remote area of Australia, while the main demand for finished metals is in the industrialised areas of the world, particularly Europe. The problem is to process the ores and move them to final markets as cheaply as possible. You can see the scope of the problem from an outline of the journey for copper, this starts with underground explosions to break up the ore body. The broken ore is collected by front-end loaders and put onto ore trains that carry it to underground crushers. The crushed ore is then hoisted to the…arrow_forwardMount Isa Mines is one of the world’s great metal mines. Its main operations are at Mount Isa, in Queensland, Australia, where it mines adjacent deposits of copper and silver-lead-zinc ores. Production levels changes with world demand and prices, but in atypical year 7 million tonnes of ore are mined to give 150,000 tonnes of copper and lead (containing silver) and 200,000 tonnes of zinc. Mount Isa has serious transport problems. It produces huge quantities of ore in a remote area of Australia, while the main demand for finished metals is in the industrialised areas of the world, particularly Europe. The problem is to process the ores and move them to final markets as cheaply as possible. You can see the scope of the problem from an outline of the journey for copper, this starts with underground explosions to break up the ore body. The broken ore is collected by front-end loaders and put onto ore trains that carry it to underground crushers. The crushed ore is then hoisted to the…arrow_forward4. Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E 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. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Set up the solution in Excel and solve with Solver. What are total costs?arrow_forward
- OCEAN: Mike plans to transport 30 pallets containing 53 cartons and an additional pallet containing 40 cartons from Montreal to Shanghai. Each pallet (including the 1 additional pallet) weighs 800kgs and measures 121cm x 90cm x 100cm. The rate is $92 w/m. Determine the Freight cost ($). 3106 2000 32.67 25.5 Othersarrow_forwardThe method for determining facility location which involves determining x and y co-ordinates of the proposed new location O a. Factor Rating Method O b. Locational Break-even Analysis O C. Transportation Method Od. Centroid Methodarrow_forwardEast Texas Seasonings began as a small business in Athens Texas. Over the years, the company's success has exceeded the capacity of this one location so Mr. Sass, the owner opened 3 additional branches. Each of these branches house a unique source of the company's secret blend. In an attempt to increase efficiency, the company is preparing to build one processing center to serve its four sources of seasonings. The 4 source locations are at the coordinates shown below. Also, the volume from each source is provided. X-coordinate Y-coordinate Volume Athens, Texas 30 40 100 Beaumont, Texas 20 15 400 Carthage, Texas 55 60 150 Denton, Texas 20 70 250 a. What are the main considerations East Texas Seasoning should look at when determining a central location? Ensure you show how these issues are related to East Texas Seasoning.arrow_forward
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