The Move-It Company has two plants producing forklift trucks that then are shipped to three distribution centers. The production costs are the same at the two plants (Plant A and Plant B), and the cost of shipping for each truck is shown for each combination of plant and distribution center: Plant A B 1 $800 $600 Distribution Center 2 $700 $800 3 $400 $500 A total of 60 forklift trucks are produced and shipped per week. Plant A can produce and ship any amount up to a maximum of 35 trucks per week, while Plant B can produce and ship any amount up to a maximum of 25 trucks per week. So, there is flexibility on how to divide the total production between the two plants so as to reduce shipping costs. However, each distribution center must receive exactly 20 trucks per week. Management's objective is to determine how many forklift trucks should be produced at each plant, and then what the overall shipping pattern should be to minimize total shipping cost. (a) Formulate a linear programming model for this problem. (max or min Z=..., subject to ... constraints...) (b) Formulate this problem as a transportation problem by constructing the appropriate parameter table. (c) Draw the network representation of this problem. (d) Use the Excel Solver to obtain an optimal solution.
The Move-It Company has two plants producing forklift trucks that then are shipped to three distribution centers. The production costs are the same at the two plants (Plant A and Plant B), and the cost of shipping for each truck is shown for each combination of plant and distribution center: Plant A B 1 $800 $600 Distribution Center 2 $700 $800 3 $400 $500 A total of 60 forklift trucks are produced and shipped per week. Plant A can produce and ship any amount up to a maximum of 35 trucks per week, while Plant B can produce and ship any amount up to a maximum of 25 trucks per week. So, there is flexibility on how to divide the total production between the two plants so as to reduce shipping costs. However, each distribution center must receive exactly 20 trucks per week. Management's objective is to determine how many forklift trucks should be produced at each plant, and then what the overall shipping pattern should be to minimize total shipping cost. (a) Formulate a linear programming model for this problem. (max or min Z=..., subject to ... constraints...) (b) Formulate this problem as a transportation problem by constructing the appropriate parameter table. (c) Draw the network representation of this problem. (d) Use the Excel Solver to obtain an optimal solution.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:The Move-It Company has two plants producing forklift trucks that then are shipped to three distribution
centers. The production costs are the same at the two plants (Plant A and Plant B), and the cost of shipping
for each truck is shown for each combination of plant and distribution center:
Plant
A
B
1
$800
$600
Distribution Center
2
$700
$800
3
$400
$500
A total of 60 forklift trucks are produced and shipped per week. Plant A can produce and ship any amount
up to a maximum of 35 trucks per week, while Plant B can produce and ship any amount up to a maximum
of 25 trucks per week. So, there is flexibility on how to divide the total production between the two plants
so as to reduce shipping costs. However, each distribution center must receive exactly 20 trucks per week.
Management's objective is to determine how many forklift trucks should be produced at each plant, and
then what the overall shipping pattern should be to minimize total shipping cost.
(a) Formulate a linear programming model for this problem. (max or min Z=..., subject to ... constraints...)
(b) Formulate this problem as a transportation problem by constructing the appropriate parameter table.
(c) Draw the network representation of this problem.
(d) Use the Excel Solver to obtain an optimal solution.
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