RVW (Restored Volkswagens) buys 30 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 20 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below. What should be shipped? Repair Shops Used Car Lots S1 S2 L1 L2 L3 500 400 S1 350 400 600 550 350 S2 450 750 550

RVW (Restored Volkswagens) buys 30 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 20 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below. What should be shipped? Repair Shops Used Car Lots S1 S2 L1 L2 L3 500 400 S1 350 400 600 550 350 S2 450 750 550

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 76P

See similar textbooks

Similar questions

Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
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…
Sunco Oil produces oil at two wells. Well 1 canproduce up to 150,000 barrels per day, and well 2 canproduce up to 200,000 barrels per day. It is possible toship oil directly from the wells to Sunco’s customersin Los Angeles and New York. Alternatively,Sunco could transport oil to the ports of Mobile andGalveston and then ship it by tanker to New Yorkor Los Angeles. Los Angeles requires 160,000 barrelsper day, and New York requires 140,000 barrels perday. The costs of shipping 1000 barrels betweenvarious locations are shown in the file P05_55.xlsx,where a blank indicates shipments that are not allowed.Determine how to minimize the transport costs inmeeting the oil demands of Los Angeles and New York.
The Hamilton County Local Government has eight sectors which need fire protection. Adequate Fire protection can be provided in each sector either by building a fire station in that sector, or by building a fire station in another sector which is no more than a 12-minute drive away. The time to drive between the centers of each pair of sectors is given in the following table. (Because of one-way streets and left turns the times are not symmetric.) The cost to build a fire station is the same in each sector. Formulate an integer programming model to choose which sectors should have their own fire station. Solve the model by using Excel Solver.
RVW (Restored Volkswagens) buys 15 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 10 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also, there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below. Given the costs below, draw a network representation for this problem. Repair Shops Used Car Lots S1 S2 L1 L2 L3 Auction 1 550 500 S1 250 300 500 Auction 2 600 450 S2 350 650 450 Formulate this problem as a linear programming model. (Note: You do not need to solve the model.)
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…
University Square Apartments is a large apartment complex located close to the University. University Square Apartments are owned and managed by a local family, the Spencers. The Spencers have several rental properties in the area. University Square Apartments have several types of units, including four-bedroom, 3-bedroom, 2 bedroom, and one bedroom apartments. The most common unit is the two-bedroom, one-bathroom unit. You and Chris are both in your third year at the University. You met each other through mutual friends and share common interests in many areas. Approximately 4 months ago, you and Chris moved into unit 4C in University Square apartments. The two of you signed a one-year lease and moved into a 2-bedroom, one-bathroom apartment. The monthly rent, which you and Chris agreed to split each month, is $1050. In the past four months, you and Chris have experienced many problems. In the past week, the situation between you and Chris reached a boiling point. You normally send in…
RVW (Restored Volkswagens) buys 30 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 20 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below. Repair Shops Used Car Lots S1 S2 L1 L2 L3500 400 S1 350 400 600550 350 S2 450 750 550
BC Petrol manufactures three chemicals at its chemical plant in Kentucky: BCP1, BCP2, and BCP3. These chemicals are produced in two production processes known as zone and man. Running the zoning process for an hour costs $48 and yields three units of BCP1, one unit of BCP2, and one unit of BCP3. Running the man process for one hour costs $24 and yields one unit of BCP1 and one unit of BCP2. To meet customer demands, at least 20 units of BCP1, 10 units of BCP2, and 6 units of BCP3 must be produced daily. Assuming a linear relationship, use Excel Solver to determine the optimal mix of processes zone and man to minimize costs and meet BC Petrol's daily demands.
Suisan Fish Company contracts with fishers in Hilo, Kona, and Puna, Big Island to purchase fishes. The fishes are cleaned and stored at the local processing facilities. Then the fishes are shipped to two plants, where they are cut, processed, and packaged as sushi and sashimi. The sushi and sashimi are then transported to three restaurants. The transportation costs per fish from the fishers to the plants and from the plants to the restaurants are summarized in the following tables: Determine the optimal shipments from fishers to plants and from plants to restaurants to minimize total transportation costs. Include the formulation and solver outputs. What would be the effect on the solutions if the capacity at each plant were 70 fishes?
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?