Two plants supply three customers with medical supplies. The unit costs of shipping from the plants to the customers, along with the supplies and demands, are given in the table below. To From Customer 1 Customer 2 Customer 3 Supply Plant 1 $55 $65 $80 35 Plant 2 $10 $15 $25 50 Demand 10 10 10 The company's goal is to minimize the cost of meeting customers" demands. Find a bfs for this transportation problem by Minimum-cost method and determine the objective value. ) 1000 p)• 2000 2 1500

Two plants supply three customers with medical supplies. The unit costs of shipping from the plants to the customers, along with the supplies and demands, are given in the table below. To From Customer 1 Customer 2 Customer 3 Supply Plant 1 $55 $65 $80 35 Plant 2 $10 $15 $25 50 Demand 10 10 10 The company's goal is to minimize the cost of meeting customers" demands. Find a bfs for this transportation problem by Minimum-cost method and determine the objective value. ) 1000 p)• 2000 2 1500

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 67P

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The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
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?
1. In a transportation problem with 4 sources and 5 destinations, how many shipping lanes will exist? 2. In a transportation problem with 3 sources and 3 destinations, how many fixed requirement constraints will be needed?
Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $13 $14 $15 2 $11 $12 $11 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 400 800 600 If the Edwards production plan for the next period includes 800 units of component 1 and 600 units of component 2, what purchases do you recommend? That is, how many units of each component should be…
An industrial system has two industries with the following input requirements. (a) To roduce $1.00 worth of output, Industry A requires $0.20 of its own products and $0.50 of industry B's products. (b) To produce $1.00 worth of output, industry B requires $0.40 of its own product and $0.30 of industry A's product. Find D, the input-output matrix for this system. D = ? Solve for the output matrix X in the equation X = DX + E where E is the external demand matrix E= [10,000] [20,000] (Round to the nearest whole number.)
A pet daycare facility offers pet sitting services where owners can drop off their pets for training and socializing with other pets. To feed the pets, the daycare makes two types of pet food. A bag of freeze-dried nuggets costs $7.99 and contains 21 units of proteins, 4 units of fiber, and 15 units of fat. A bag of dehydrated nuggets costs $11.26 and contains 28 units of proteins, 7 units of fiber, and 20 units of fat. The minimum daily requirements are usually 200 units of protein, 75 units of fiber, and 220 units of fat. Formulate the information as an LP problem and answer the following questions. How many bags of freeze-dried nuggets and dehydrated food should the facility make each day to minimize the total cost? What is the lowest cost? Identify the binding and non-binding constraints and report the surplus values.
A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Factory (capacity) Customer 1 (125) Customer 2 (150) Customer 3 (175) Customer 4 (75) A (100) $ 15 $ 10 $ 20 $ 17 B (75) $ 20 $ 12 $ 19 $ 20 C (100) $ 22 $ 20 $ 25 $ 14 D (250) $ 21 $ 15 $ 28 $ 12 How many supply nodes are present in this problem? Multiple Choice: 4 3 1 8 16
Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $12 $12 $15 2 $11 $10 $12 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 575 950 800 If the Edwards production plan for the next period includes 1050 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be…
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Number ofFans Number ofCooling Coils ManufacturingTime (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 220 fan motors, 340 cooling coils, and 2,600 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E + 95S + 135D s.t. 1E + 1S + 1D ≤ 220 Fan motors 1E + 2S + 4D ≤ 340 Cooling coils 8E + 12S + 14D ≤ 2,600 Manufacturing time E, S, D ≥ 0 The computer solution is shown below. Optimal Objective Value = 17700.00000…
Polly Astaire makes fine clothing for big and tall men. A fewyears ago Astaire entered the sportswear market with theSunset line of shorts, pants, and shirts. Management wants tomake the amount of each product that will maximize profits.Each type of clothing is routed through two departments, Aand B. The relevant data for each product are as follows: Department A has 120 hours of capacity, department B has160 hours of capacity, and 90 yards of material are available.Each shirt contributes $10 to profits and overhead; each pairof shorts, $10; and each pair of pants, $23.a. Specify the objective function and constraints for thisproblem.b. Use a computer package such as POM for Windows tosolve the problem.c. How much should Astaire be willing to pay for an extrahour of department A capacity? How much for an extrahour of department B capacity? For what range of right-hand values are these shadow prices valid?
Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pen...Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.Fliptop Model Tiptop Model AvailablePlastic 3 4 36Ink Assembly 5 4 40Molding Time 5 2 30The profit for either model is $1000 per lot.What is the linear programming model for this problem?What are the boundary points of the feasible region?What is the profitability at each boundary point of the feasible region?Find the optimal solution.