Widgetco manufactures widgets at two factories, one in Memphis and one in Denver. TheMemphis factory can produce as many as 150 widgets per day, and the Denver factory canproduce as many as 200 widgets per day. Widgets are shipped by air to customers in LosAngeles and Boston. The customers in each city require 130 widgets per day. Because of thederegulation of airfares, Widgetco believes that it may be cheaper to first fly some widgets toNew York or Chicago and then fly them to their final destinations. The costs of flying awidget are shown below. Widgetco wants to minimize the total cost of shipping the requiredwidgets to its customers.To ($)NewLosMemphisDenverChicagoBostonYorkAngelesMemphis8132528Denver15122625New1617YorkFromChicago61416LosAngelesBostonFormulate the linear programming model of the transshipment problem.6

Linear programming, often known as linear optimization, is a method for obtaining the best result…

Answered: Widgetco manufactures widgets at two…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 53P

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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?
Fairway Inc. makes custom golf clubs. They are manufactured in 3 plants in Denver, Phoenix, and Dallas. They are then shipped to distribution centers in Sacramento, Salt Lake, Chicago, Albuquerque, and New York. Since shipping costs are a major expense, management requires an analysis to determine the optimal shipping routes and quantities shipped along those routes. Each plant has a maximum production capacity and each distribution center has a demand that must be satisfied. You must determine how many clubs to send along each route, staying within plant capacity, meeting demand, for the lowest total shipping cost. Shipping Costs per route Plants Sacramento Salt Lake Chicago Albeq New York Capacity Denver $10 $8 $6 $5 $4 310 Phoenix $6 $5 $4 $3 $6 260 Dallas $3 $4 $5 $5 $9 280 Demand 180 80 200 160 220 Number to ship from plant to warehouse: Plants Sacramento Salt Lake Chicago Albeq New York Total Shipped Denver Phoenix…
The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 75% mild cheddar and 25% extra sharp, and the Zesty blend contains 70% mild cheddar and 30% extra sharp. This year, a local dairy cooperative offered to provide up to 8500 pounds of mild cheddar cheese for $1.40 per pound and up to 2700 pounds of extra sharp cheddar cheese for $1.60 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.40 per container. If each container of Regular is sold for $2.20 and each container of Zesty is sold for $2.00, how many containers of Regular and Zesty should New England Cheese produce? Do not round your interim computations. If required, round your answers to the nearest whole number. Let R = number of containers of Regular Z =…
The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 80% mild cheddar and 20% extra sharp, and the Zesty blend contains 60% mild cheddar and 40% extra sharp. This year, a local dairy cooperative offered to provide up to 7,980 pounds of mild cheddar cheese for $1.20 per pound and up to 2,970 pounds of extra sharp cheddar cheese for $1.40 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.20 per container. If each container of Regular is sold for $1.90 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce? *This is a Linear Programming problem, can you show me how to find the constraints and solve*
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.
State University must purchase 1,100 computers from three vendors. Vendor 1 charges $500 per computer plus a delivery charge of $5,000. Vendor 2 charges $350 per computer pluse a delivery charge of $4,000. Vendor 3 chargest $250 per computer pluse a delivery charge of $6,000. Vendor 1 will sell the university at most 500 computers; vendor 2 at most 900; and vendor 3 at most 400. Formulate an IP to minimize the cost of purchasing the needed computers.
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 town of Lexington purchases gasoline from three vendors to fuel its fleet of municipal vehicles. Each vendor delivers gasoline in 6,000 gallon quantities. Since vendors must deliver the fuel, a transportation fee (based on the distance the vendor must travel) is added to each delivery. The number of deliveries required by each location, the cost of supplying a truckload of gasoline to each location from each vendor, and the number of truckloads each vendor can deliver are provided below: PoliceStation FireStation BusDepot PublicWorksGarage Deliveries(truckloads)available Vendor A Vendor B Vendor C Deliveries(truckloads)required $500 $350 $400 12 $525 $425 $375 2 $550 $450 $625 18 $600 $575 $475 6 20 14 10 Assuming that the price per gallon of fuel is the same for each vendor, develop a linear programming model that minimizes the total transportation fee that Lexington must pay for supplying all of its facilities’ fuel needs.
A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D). For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (attached image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: The picture is in spanish, but I mean... is pretty easy to understand
A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D). For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (attached image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: do the exercise by hand, or do it digitally, but not in excel.
The Scottsville Textile Mill produces several different fabrics on eight dobby looms that operate 24 hours per day and are scheduled for 30 days in the coming month. The mill will produce only Fabric 1 and Fabric 2 during the coming month. Each dobby loom can turn out 4.62 yards of either fabric per hour. Assume that there is a monthly demand of 16,000 yards of Fabric 1 and 12,000 yards of Fabric 2. Profits are calculated as 33¢ per yard for each fabric produced on the dobby looms. (a) Will it be possible to satisfy total demand? (b) In the event that total demand is not satisfied, the Scottsville Textile Mill will need to purchase the fabrics from another mill to make up the shortfall. Its profits on resold fabrics ordered from another mill amount to 20¢ per yard for Fabric 1 and 16¢ per yard for Fabric 2. How many yards of each fabric should it produce to maximize profits? (Round your answers to one decimal place. If total demand is satisfied, enter NONE.)
The Scottsville Textile Mill produces several different fabrics on eight dobby looms that operate 24 hours per day and are scheduled for 30 days in the coming month. The mill will produce only Fabric 1 and Fabric 2 during the coming month. Each dobby loom can turn out 4.65 yards of either fabric per hour. Assume that there is a monthly demand of 16,000 yards of Fabric 1 and 12,000 yards of Fabric 2. Profits are calculated as 33¢ per yard for each fabric produced on the dobby looms. Will it be possible to satisfy total demand? (a)Yes, the mill can produce enough to meet the demand. (b)No, the mill can not produce enough to meet the demand. In the event that total demand is not satisfied, the Scottsville Textile Mill will need to purchase the fabrics from another mill to make up the shortfall. Its profits on resold fabrics ordered from another mill amount to 20¢ per yard for Fabric 1 and 16¢ per yard for Fabric 2. How many yards of each fabric should it produce to maximize…

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