1) Transportation costs for Legos are give in the following chart (see right): D
ID: 459675 • Letter: 1
Question
1) Transportation costs for Legos are give in the following chart (see right):
Distribution centers are across the top row; plants creating legos are in the left column
Washington
New York
Ohio
Michigan
SUPPLY
California
$5.00
$15.00
$12.00
$11.50
20000
Texas
$8.00
$12.00
$6.00
$7.00
25000
Florida
$17.00
$7.00
$7.00
$9.00
15000
Minnesota
$12.00
$12.00
$5.00
$4.00
12500
DEMAND
30000
30000
10000
10000
(a) How should the legos be shipped to satisfy demand and minimize cost? Provide detailed solution with analysis.
(b) Suppose that you consider building a new source to satisfy demand. Choose a location and assign values for shipping to the 4 destinations. Assuming the production levels of this new facility put supply equal to demand in the table above, how should the legos be shipped to minimize costs? Comment on the change in shipping plans from what you found previously.
1) Transportation costs for Legos are give in the following chart (see right):
Distribution centers are across the top row; plants creating legos are in the left column
Washington
New York
Ohio
Michigan
SUPPLY
California
$5.00
$15.00
$12.00
$11.50
20000
Texas
$8.00
$12.00
$6.00
$7.00
25000
Florida
$17.00
$7.00
$7.00
$9.00
15000
Minnesota
$12.00
$12.00
$5.00
$4.00
12500
DEMAND
30000
30000
10000
10000
(a) How should the legos be shipped to satisfy demand and minimize cost? Provide detailed solution with analysis.
(b) Suppose that you consider building a new source to satisfy demand. Choose a location and assign values for shipping to the 4 destinations. Assuming the production levels of this new facility put supply equal to demand in the table above, how should the legos be shipped to minimize costs? Comment on the change in shipping plans from what you found previously.
Explanation / Answer
a) Solving the given problem in solver:
Where the table 2 gives us the shipping quantities to satisfy the demand, and the total cost gives us the minimum total cost incurred in shipping these quantiies.
(Constraints are the total shipping from indivisual distribution centers should be >= demand, and the total production from each plant should be <= possible supply. Also, the changing cells, i.e. the shipping quantities should >= 0 and integer)
(Objective function is to minimize the total cost, which is the sum of all the products of unit transportation costs and shipped quantities)
b)
The total shipping costs are lower than in the case of the 4 distributors, also earlier the distributor in Washington was shipping to 4 locations, which is now reduced to maximum 2 locations being served by each distributor
Transportation Costs Washington New York Ohio Michigan California 5 15 12 11.5 Texas 8 12 6 7 Florida 17 7 7 9 Minnesota 12 12 5 4 Washington New York Ohio Michigan TOTAL SIGN SUPPLY California 0 7500 10000 2500 20000 <= 20000 Texas 2500 22500 0 0 25000 <= 25000 Florida 15000 0 0 0 15000 <= 15000 Minnesota 12500 0 0 0 12500 <= 12500 TOTAL 30000 30000 10000 2500 SIGN >= >= >= >= DEMAND 30000 30000 10000 10000 Total cost $ 956250Related Questions
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