In dealing with a transportation problem, what should be always observed? O The demand of the destination should always be larger than the capacity of the source. O The total number of units coming out of a source must not exceed the capacity of the source. O The total number of units incoming to the destination must not exceed to the demand of that destination. O The capacity of the source should always be greater than the demand.
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- Formulate and then solve a linear programming model of this problem, to determine how manycontainers of each product to produce tomorrow to maximize profits. The company makes fourjuice products using orange, grapefruit, and pineapple juice.Product Retail Price per QuartOrange juice $1.00Grapefruit juice .90Pineapple juice .80All-in-One 1.10The All-in-One juice has equal parts of orange, grapefruit, and pineapple juice. Each product isproduced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orangejuice, 300 gallons of grapefruit juice, and 200 gallons of pineapple juice. The cost per gallon is$2.00 for orange juice, $1.60 for grapefruit juice, and $1.40 for pineapple juice.In addition, the manager wants grapefruit juice to be used for no more than 30 percent of thenumber of containers produced. She wants the ratio of the number of containers of orange juice tothe number of containers of pineapple juice to be at least 7 to 5.A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.A company supplies goods to three customers, who eachrequire 30 units. The company has two warehouses.Warehouse 1 has 40 units available, and warehouse 2 has 30units available. The costs of shipping 1 unit from warehouseto customer are shown in Table 7. There is a penalty for eachunmet customer unit of demand: With customer 1, a penaltycost of $90 is incurred; with customer 2, $80; and withcustomer 3, $110. Formulate a balanced transportationproblem to minimize the sum of shortage and shipping costs.
- Explain why it is problematic to include a constraint such as the following in an LP model for a blending problem: Total octane in gasoline 1 blend/Barrels of gasoline 1 blend daily ≥ 10A wholesaler is to transport 840 crates of soda from the factory to his shop. He has a lorry which can carry 150 crates at a time and a pick-up which can carry 60 crates at a time. The cost of each journey for the lorry is Shs 25,000 and for the pick-up, it is Shs 20,000. Due to time constraint, the pick-up is to make more journeys than the lorry because it travels faster. He has Shs 250,000 available for transportation. having had the knowledge of linear programming ,advise how he can organize his vehicles to keep the cost as low as possible and state how much he saves by making these journeys.Federated Oil has refineries in Los Angeles and Chicago. The Los Angeles refinery can refine up to two million barrels of oil per year, and the Chicago refinery up to three million. After the oil is refined, it is shippedto two distribution points, Houston and New York City. Federated Oil estimates that each distribution point can sell up to five million barrelsper year. Because of differences in shipping and refining costs, the profit earned (in dollars) per million barrels of oil shipped depends on where the oil was refined and on the point of distribution. This information is listed in the file P04_69.xlsx. The company is considering expanding the capacity of each refinery.Each million barrels of annual refining capacity that isadded will cost $120,000 for the Los Angeles refinery and $150,000 for the Chicago refinery. Determine how Federated Oil can maximize its profit (including expansion costs) over a 10-year period.
- Constraints limit the degree to which the objective in a linear programming problem is satisfied. TRUE OR FALSEA call center employs 1,425 agents. Every month 57 employees leave the company and 57 new employees are hired. a. How long on average does an agent work for this call center (in months) Suppose the cost of hiring and training a new agent is $1,140. The manager of this call center believes that increasing agents’ salaries would keep them working longer at the company. The manager wants to increase the average time that an agent works for the call center to 36 months, or three years. b-1. Given the current average working time for agents at this call center, determine the current annual cost for hiring and training. b-2. Assuming the average time that an agent works for the call center is increased to 36 months, determine the new annual cost for hiring and training. b-3. If the time an agent works for the call center is increased to 36 months on average, how much could the company save on hiring and training costs over a year?A company manufactures two types of trucks. Eachtruck must go through the painting shop and the assembly shop. If the painting shop were com-pletely devoted to painting type 1 trucks, 650 per day could be painted, whereas if the painting shopwere completely devoted to painting type 2 trucks,550 per day could be painted. If the assembly shopwere completely devoted to assembling truck 1engines, 1400 per day could be assembled, whereasif the assembly shop were completely devoted toassembling truck 2 engines, 1000 per day could beassembled. It is possible, however, to paint bothtypes of trucks in the painting shop. Similarly, it ispossible to assemble both types in the assemblyshop. Each type 1 truck contributes $2500 to profit; each type 2 truck contributes $3000. Use Solver to maximize the company’s profit. (Hint: One ap-proach, but not the only approach, is to try a graphi-cal procedure first and then deduce the constraints from the graph.)
- What function does linear programming play in OR?A company has four warehouses and six stores. The warehouses altogether have a surplus of 22 units of a given commodity, divided among them as follows: Warehouses 1 2 3 4 Surplus 5 6 2 9 The six stores altogether need 22 units of the commodity. Individual requirements at b stores 1,2,3,4,5 and 6 are 4,4,6,2,4 and 2 units respectively. Cost of shipping one unit of commodity from warehouse i to store j in $ dollars is given in the matrix below. Stores Warehouses 1 2 3 4 5 6 1 9 12 9 6 9 10 2 7 3 7 7 5 5 3 6 5 9 11 3 11 4 6 8 11 2 2 10 Required Formulate the mathematical model for the problem How should the products be shipped from the warehouses to the stores so that the transportation cost is minimum?TRUE OR FALSE Each constraint excluding nonnegativity constraints, in the mathematical formulation of a linear program generates one row in the simplex table.