Assignment
1. The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1,2 and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distribution centers is given below: (Read pp. 425-431 & pp.480-484) (30 points)
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Distance to Distribution Center (Mile)
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|
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1
|
2
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3
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4
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Plant
|
|
|
|
|
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1
|
800
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1,300
|
750
|
700
|
|
2
|
1100
|
1,400
|
900
|
1,100
|
|
3
|
600
|
1,300
|
800
|
900
|
The freight cost for each shipment is $85 plus 55 cents mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost? Formulate this problem as a transportation problem on a spreadsheet and then use the Excel Solver to obtain an optimal solution. Also, interpret the results using at least 150 words by addressing the following issues. Also, please make sure you provide answer report you obtained from Excel Solver.
a. What is the optimal mix of shipments from each plant to each of the distribution center?
b. What is the minimum cost that could be achieved?
2. The following table shows the unit shipping cost between cities, the supply at each source city and demand at each destination city.
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Source
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Destination
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Supply
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Terre Haute
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Indianapolis
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Ft. Wayne
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South Bend
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St. Louis
|
8
|
6
|
12
|
9
|
100
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Evansville
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5
|
5
|
10
|
8
|
100
|
|
Bloomington
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3
|
2
|
9
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10
|
100
|
|
Demand
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150
|
60
|
45
|
45
|
|
a. Given this table, set up a linear programming model for this transportation problem
b. Provide the optimal solution using Solver in Excel. You must provide the optimal unit of products shipped from each source city to each destination city, and total minimum cost
c. Discuss any biblical principles that could be relevant to business issues (This is an open- ended question and therefore there is no definite answer.)