A rock group plans to travel for a total of 33 weeks, making three concert stops. They will be in Japan for 5 more weeks than they will be in Australia. Their stay in Sweden will be 2 weeks shorter than that in Australia. How many weeks will they be in each country?
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)General Ford has two plants, two warehouses, and threecustomers. The locations of these are as follows:Plants: Detroit and AtlantaWarehouses: Denver and New YorkCustomers: Los Angeles, Chicago, and PhiladelphiaCars are produced at plants, then shipped to warehouses,and finally shipped to customers. Detroit can produce 150cars per week, and Atlanta can produce 100 cars per week.Los Angeles requires 80 cars per week; Chicago, 70; andPhiladelphia, 60. It costs $10,000 to produce a car at eachplant, and the cost of shipping a car between two cities isgiven in Table 62. Determine how to meet General Ford’sweekly demands at minimum cost.Universal Exports has four factories where it makes potato mashers. These are sent to each of four retail outlets. The cost (in thousand pesos) of shipping a case from each source to each destination is given below. Each of the factories can produce 100 units while the demand at A is 80 units, B is 70 units, C is 120 units, and D is 100 units. How many units must be transported from Factory 1 to retail outlet D?
- A company imports goods at two ports: Philadelphia and New Orleans. Shipments of one product are made to customers in Atlanta, Dallas, Columbus, and Boston. For the next planning period, the supplies at each port, customer demands, and shipping costs per case from each port to each customer are as follows: Customers Port Atlanta Dallas Columbus Boston Port Supply Philadelphia 2 6 6 2 5,000 New Orleans 1 2 5 7 3,000 Demand 1,400 3,200 2,000 1,400 Develop a network representation of the distribution system. Develop the objective function and the constraints.Airline Scheduling. Alpha Airline wishes to schedule no more than one flight out of a given airport to each of the following cities: C, D, L, and N. The available departure slots are 8 a.m., 10 a.m., and 12 noon. Alpha leases the airplanes at the cost of $5000 before and including 10 a.m. and $3000 after 10 a.m., and is able to lease at most two per departure slot. Also, if a flight leaves for location N in a time slot, there must be a flight leaving for location L in the same time slot. The expected profit (in $1000) contribution before rental costs per flight is shown in the table below. Time Slot 8 10 12 C 10 6 6 D 9 10 9 L 14 11 10 N 18 15 10 a) Formulate an integer linear program model that can be used to find the profit-maximizing schedule. Define your decision variables as Xij = 1 if a flight to destination i occurs in time slot j and Xij = 0 otherwise; and Yj = number of airplanes rented for time slot j. Write the objective function and all the constraints. b)…The Sav-Us Rental Car Agency has six lots in Nashville, and it wants to have a certain number of cars available at each lot at the beginning of each day for local rental. The agency would like a model it could quickly solve at the end of each day that would tell it how to redistribute the cars among the six lots in the minimum total time. The times required to travel between the six lots are as follows: To (min.) From 1 2 3 4 5 6 1 12 17 18 10 20 2 14 10 19 16 15 3 14 10 12 8 9 4 8 16 14 12 15 5 11 21 16 18 10 6 24 12 9 17 15 The agency would like the following number of cars at each lot at the end of the day. Also, shown is the number of available cars at each lot at the end of a particular day. Determine the optimal reallocation of rental cars. Lot (cars) Cars 1 2 3 4 5 6 Available 37 20 14 26 40 28…
- You own a wheat warehouse with a capacity of 20 bushelsAt the beginning of month 1, you have 6 bushels of wheat. Each month, wheat can be bought and sold at the prices per one bushel shown in the above table. The sequence of events during each month is as follows: You observe your initial stock of wheat. You can sell any amount of wheat up to your initial stock at the current month's selling price. You can then buy much wheat as you want , subject to the warehouse capacity Determine how to maximize the profit earned over the next 10 months. Need to use only excel for this questionBaseball umpiring crews are currently in four cities where three-game series are beginning. When these are finished, the crews are needed to work games in four different cities. The distances (miles) from each of the cities where the crews are currently working to the cities where the new games will begin are shown in the following table. The X indicates that the crew in Oakland cannot be sent to Toronto. Formulate as a linear programming problem to minimize the miles traveled. HINT: Since one assignment cannot be made, what are the options for that variable in the formulation? Solve using Excel solver. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints.…
- 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?A travelling salesman, named Magan Shah plans to visit five cities 1, 2, 3, 4 and 5. The travel time (in hours) between these cities is shown below. To city 1 2 3 4 5 From city 1 x 5 8 4 5 2 5 x 7 4 5 3 8 7 x 8 6 4 4 4 8 x 8 5 5 5 6 8 x How should he schedule his touring plan in order to minimize the total travel time, if he visits each city once a week?Fowle Marketing Research, Inc. is faced with the problem of assigning three available project leaders (agents) to each of three new research studies (tasks). Fowle’s management realizes, however, that the time required to complete each study will depend on the experience and ability of the project leader assigned to the study. Since the three studies have been judged to have approximately the same priority, the company would like to determine the assignments that will minimize the total number of days required to complete all three. If a project leader is to be assigned to one and only one client, what assignments should be made (optimal solutions)? How many days are required (objective function value).With three project leaders and three clients, there are total of nine possible assignment alternatives. The alternatives and the estimated project completion times in days are summarized in Table Client Project Leader 1 2…