The blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to The supply and demand for donated blood is shown in the figure below along with the unit cost of shipping along each possible arc. cost. (Let X₁, represent the number of units that flow from node i to node j.) Pittsburgh 300 Charleston Richmond 800

Practical Management Science
6th Edition
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Author:WINSTON, Wayne L.
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Chapter2: Introduction To Spreadsheet Modeling
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The blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk.
The supply and demand for donated blood is shown in the figure below along with the unit cost of shipping along each possible arc. The goal is to meet the expected demand at the lowest possible
cost. (Let X;; represent the number of units that flow from node i to node j.)
Pittsburgh
-1,300
1
Staunton
-1,200 2
LO
Charleston
3
5
Roanoke
300
3
7 7
200
LO
Richmond
5
(X13X14 X231 X24¹ X34¹ X35¹ X36¹ X43¹ X46¹ X47, X56, X67) =
6
=
Norfolk
800
(a) Create a spreadsheet model for this problem. What is the optimal solution?
5
6
3
700
2
Suffolk
7
400
(b) Suppose that no more than 1,000 units of blood can be transported over any one arc. What is the optimal solution to this revised problem?
(X13, X14¹ X23¹ X241 X341 X351 X361 X431 X46¹ X47, X56, X67)
Transcribed Image Text:The blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in the figure below along with the unit cost of shipping along each possible arc. The goal is to meet the expected demand at the lowest possible cost. (Let X;; represent the number of units that flow from node i to node j.) Pittsburgh -1,300 1 Staunton -1,200 2 LO Charleston 3 5 Roanoke 300 3 7 7 200 LO Richmond 5 (X13X14 X231 X24¹ X34¹ X35¹ X36¹ X43¹ X46¹ X47, X56, X67) = 6 = Norfolk 800 (a) Create a spreadsheet model for this problem. What is the optimal solution? 5 6 3 700 2 Suffolk 7 400 (b) Suppose that no more than 1,000 units of blood can be transported over any one arc. What is the optimal solution to this revised problem? (X13, X14¹ X23¹ X241 X341 X351 X361 X431 X46¹ X47, X56, X67)
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