Metro Water District is an agency that administers water distribution in a large geographic region. The region is arid, so water must be brought in from outside the region. There are three sources of imported water, which are Colombo River, Sacron River, and Calorie River. Four cities is in need of water, which are city Berdoo, Los Devils, San Go, and Hollyglass. The cost for taking water from each river and sending water to each city is different, shown in the following table. Metro Water Company wants to minimize the total cost when distributing the needed water. How much water should Metro take from each river, and how much should they send from each river to each city?
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- General Ford produces cars at L.A. and Detroit and hasa warehouse in Atlanta; the company supplies cars tocustomers in Houston and Tampa. The cost of shipping a carbetween points is given in Table 60 (“—” means that ashipment is not allowed). L.A. can produce as many as1,100 cars, and Detroit can produce as many as 2,900 cars.Houston must receive 2,400 cars, and Tampa must receive1,500 cars.a Formulate a balanced transportation problem thatcan be used to minimize the shipping costs incurred inmeeting demands at Houston and Tampa.b Modify the answer to part (a) if shipments betweenL.A. and Detroit are not allowed.c Modify the answer to part (a) if shipments betweenHouston and Tampa are allowed at a cost of $5.TRANSPORTATION PROBLEM The freight cost for each shipment is $100 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping costs? Use Northwest Corner Cell Method, Least Cost Cell Method and VAM in solving for the optimal solution.The High-Price Oil Company owns a pipeline network that is used to convey oil from its source to several storage locations. A portion of the network is as follows: Due to the varying pipe sizes, the flow capacities vary. By selectively opening and closing sections of the pipeline network, the firm can supply any of the storage locations. a. If the firm wants to fully utilize the system capacity to supply storage location 7, how long will it take to satisfy a location 7 demand of 100,000 gallons? What is the maximal flow for this pipeline system? b. If a break occurs on line 2–3 and that line is closed down, what is the maximal flow for the system? How long will it take to transmit 100,000 gallons to location 7?
- General Ford has two plants, two warehouses, and three customers. The locations of these as follows: Plants: Detroit and Atlanta;Warehouses: Denver and New YorkCustomers: Los Angeles, Chicago, and Philadelphia Cars are produced at plants, then shipped to warehouses, and finally shipped to customers. Detroit can produce 142 cars per week, and Atlanta can produce 86 cars per week. Los Angeles requires 50 cars per week; Chicago, 52; and Philadelphia 84. It costs $9500 to produce a car in Detroit and $7500 to produce a car in Atlanta, and the costs of shipping a car between cities are given in the table below. What is the minimal cost of meeting General Ford's weekly demands?The Acme Company operates four factories that ship products to five warehouses. The shipping costs, requirements capacities, and optimal allocations are shown below. Factory Shipping Cost per Case to Warehouses Capacity W1 W2 W3 W4 W5 F1 $1.50 $4.50 $6.00 $7.50 $9.00 40,000 30,000 10,000 F2 $3.00 $3.00 $1.50 $6.00 $7.50 30,000 25,000 5,000 F3 $1.50 $7.50 $1.50 $4.50 $1.50 30,000 10,000 20,000 F4 $7.50 $3.00 $6.00 $7.50 $6.00 25,000 25,000 Demand 30,000 35,000 25,000 15,000 20,000 125,000 What is the total cost of the optimal solution? Total cost = $nothing. (Enter your response to the nearest dollar.)Paul Bergey is in charge of loading cargo ships for International Cargo Company (ICC) at the port in Newport News, Virginia. Paul is preparing a loading plan for an ICC freighter destined for Ghana. An agricultural commodities dealer wants to transport the following products aboard this ship. Commodity A B C D Amount Available (tons)4,8002,5001,2001,700 Volume per Ton (cubic feet) 40256055 Profit per Ton ($)70506080 Paul can elect to load any and/or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions. Cargo Hold Forward Center Read Weight Capacity (tons) 3,000 6,000 4,000 Volume Capacity (cubic feet) 145,000 180,000 155,000 More 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% of the weight in the rear cargo hold, and the center cargo hold must be between 40% and 60% of the total…
- FiberTech makes newsprint for newspapers at three mills, A,B, and C. Th e cost of producing newsprint is estimated to be $210 atmill A, $225 at B, and $220 at C. Five primary geographical marketsare served from these mills. Th e monthly demand at each market,the shipping cost (per ton) between each mill and market, and themonthly production capacity of each mill are given in the table FiberTech would like to assign production responsibilities tothe mills, and also specify how much should be shipped fromeach plant to each market, so as to minimize total production anddistribution costs.(a) Formulate an LP to minimize total production anddistribution costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.Cutey Barber Salon is a trendy barber salon that is located in a densely populated city called Maple.Demand for the services offered by the salon is fairly high. It offers services such as haircuts, hairstyling, scalp massaging and conditioning treatment, straight razor and wet shave, beard sculpting,facials and hair colouring. In addition to these services provided, the salon sells premium hair productsto customers. The salon has the ability to produce a maximum of 20,000 haircuts and hairstyling peryear. Demand for haircuts and hairstyling over the last five years can be seen in the following table:- Year Demand for haircutsand hairstyling2017 11,5002018 12,2002019 13,4002020 14,0002021 14,500 Although the business does not have a written vision and mission statement, it is clear in the minds…Cutey Barber Salon is a trendy barber salon that is located in a densely populated city called Maple.Demand for the services offered by the salon is fairly high. It offers services such as haircuts, hairstyling, scalp massaging and conditioning treatment, straight razor and wet shave, beard sculpting,facials and hair colouring. In addition to these services provided, the salon sells premium hair productsto customers. The salon has the ability to produce a maximum of 20,000 haircuts and hairstyling peryear. Demand for haircuts and hairstyling over the last five years can be seen in the following table:- Year Demand for haircuts and hairstyling 2017 11,500 2018 12,200 2019 13,400 2020 14,000 2021 14,500 Although the business does not have a written vision and mission statement, it is clear in the minds ofmanagement what they want to achieve and what they would like to be in the future.Currently, customers can walk in at any time to be served. At times, customers have to…
- Cutey Barber Salon is a trendy barber salon that is located in a densely populated city called Maple.Demand for the services offered by the salon is fairly high. It offers services such as haircuts, hairstyling, scalp massaging and conditioning treatment, straight razor and wet shave, beard sculpting,facials and hair colouring. In addition to these services provided, the salon sells premium hair productsto customers. The salon has the ability to produce a maximum of 20,000 haircuts and hairstyling peryear. Demand for haircuts and hairstyling over the last five years can be seen in the following table:- Year Demand for haircutsand hairstyling2017 11,5002018 12,2002019 13,4002020 14,0002021 14,500 Although the business does not have a written vision and mission statement, it is clear in the minds…Cutey Barber Salon is a trendy barber salon that is located in a densely populated city called Maple.Demand for the services offered by the salon is fairly high. It offers services such as haircuts, hairstyling, scalp massaging and conditioning treatment, straight razor and wet shave, beard sculpting,facials and hair colouring. In addition to these services provided, the salon sells premium hair productsto customers. The salon has the ability to produce a maximum of 20,000 haircuts and hairstyling peryear. Demand for haircuts and hairstyling over the last five years can be seen in the following table:- Year Demand for haircutsand hairstyling2017 11,5002018 12,2002019 13,4002020 14,0002021 14,500 Although the business does not have a written vision and mission statement, it is clear in the minds…Cutey Barber Salon is a trendy barber salon that is located in a densely populated city called Maple.Demand for the services offered by the salon is fairly high. It offers services such as haircuts, hairstyling, scalp massaging and conditioning treatment, straight razor and wet shave, beard sculpting,facials and hair colouring. In addition to these services provided, the salon sells premium hair productsto customers. The salon has the ability to produce a maximum of 20,000 haircuts and hairstyling peryear. Demand for haircuts and hairstyling over the last five years can be seen in the following table:- Year Demand for haircuts and hairstyling2017 11,5002018 12,2002019 13,4002020 14,0002021 14,500 Although the business does not have a written vision and mission statement, it is clear in the minds ofmanagement what they want to achieve and what they would like to be in the future. Currently, customers can walk in at any time to be served. At…