Problem 1: (Transportation Model)
For the example given in class, there are 2 supply locations and 3 demand locations, and the quantity supplied and demanded in each location, and the unit shipping cost are given below:
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Quantity Supplied
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Supply Center
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Demand Center
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Quantity Demanded
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|
500
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A. Davis
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1. SF
|
400
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|
750
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A. Bakersfield
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1. LA
|
550
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|
|
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1. SD
|
300
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Supply Center Demand Center Unit Shipping Cost
A. Davis 1 - SF $5
2 - LA $9
3 - SD $12
B. Bakersfield 1 - SF $11
2 - LA $3
3 - SD $5
(a) Set up and Solve the LP problem using Solver; Print the answer and sensitivity report;
(b) Fill out the following table:
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Consumer's Willingness to Pay for receiving one unit of the product
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SF
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|
|
LA
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|
|
SD
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|
|
|
Supplier's Willingness to Accept for shipping one unit of the product
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Davis
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|
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Bakersfield
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|
(c) What is the MB (or the value-added) of shipping one unit from Bakersfield to SF? What is the MC of shipping one unit from Davis to SF? What is the optimal shipment from Bakersfield to SF? Why?
(d) What is the MB (or the value-added) of shipping one unit from Davis to San Diego? What is the MC of shipping one unit from Davis to San Diego? What is the optimal shipment from Davis to San Diego? Why?
(e) What is the MB (or the value-added) of shipping one unit from Bakersfield to LA? What is the MC of shipping one unit from Bakersfield to LA? Why the optimal shipment from Bakersfield to SF is greater than zero?
Meaning of the "Reduced Cost" Column in Sensitivity Report
(f) If the Supplier in Bakersfield has to ship one unit to SF, what is the change in TC?
(g) If the Supplier in Davis has to ship one unit to San Diego, what is the change in TC?
Economic Meaning of yA, yB (Shadow price of supply constraints, or WTA))
(h) If the shipment from Bakersfield increases by 50 units, what will happen to TC? Why?
(i) If the shipment from Bakersfield increases by 150 units, what will happen to TC? Why?
Economic Meaning for V1, V2, V3 (Shadow price of demand constraints, or WTP)
(j) If demand in LA decreases by 50 units, what will happen to TC? Why?
(k) If demand in LA decreases by 150 units, what will happen to TC? Why?