Question 1: A company has three new machines of different types. There are four different plants that could receive the machines. Each plant can only receive one machine, and each machine can only be given to one plant. The expected profit that can be made by each plant if assigned a machine is as follows:
|
|
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Plant
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|
|
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1
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2
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3
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4
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1
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13
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16
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12
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11
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|
Machine 2
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15
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0
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13
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20
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3
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5
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7
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10
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6
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This is a transportation problem with all supplies and demands equal to 1, so it is an assignment problem. Solve this assignment problem manually (Without any software).
[Note that a balanced problem must have the same number of supplies and demands, so you must add a dummy machine (corresponding to receiving no machine) and assign a zero cost for assigning the dummy machine to a plant.]
Question 2: Thomas Industries and Washburn Corporation supply three firms (Zrox, Hewes, Rockwright) with customized shelving for its offices. They both order shelving from the same two manufacturers, Arnold Manufacturers and Supershelf, Inc.
Currently weekly demands by the users are 100 for Zrox, 70 for Hewes, and 50 for Rockwright. Arnold can supply atmost 120 units and Supershelf can supply at most 100 units to its customers.
Because of long standing contracts based on past orders, unit costs from the manufacturers to the suppliers are:
ThomasWashburn
Arnold 49
Supershelf 7 5
The costs to install the shelving at the various locations are:
ZroxHewesRockwright
Thomas 1 67
Washburn 3 4 3
Find the quantities to be shipped from each source to each destination to minimize the total shipping cost.