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Question 4:
Oranges are grown, picked, and then processed and packaged atproduction centers in Sargodha,
Risalpur, and Sahiwal. These centers supply oranges to thecompany’s distributors each month in
Peshawar, Lahore, Multan, Faisalabbad, Karachi and Quetta.
Supplier Monthly Supply (Tons)
A. Sargodha 4,000
B. Risalpur 5,000
C. Sahiwal 3,500
12,500
The distributors, spread throughout six cities, have the followingtotal monthly demand:
Distributor Monthly Demand (Tons)
1. Peshawar 1800
2. Lahore 2100
3. Multan 1700
4. Faisalabbad 1050
5. Karachi 2350
6. Quetta 1400
10,400
The company must pay the following shipping costs per ton:
to
from 1 2 3 4 5 6
A. $0.50 $0.35 $0.60 $0.45 $0.80 $0.75
B. 0.25 0.65 0.40 0.55 0.20 0.65
C. 0.40 0.70 0.55 0.50 0.35 0.50
(a) Determine the minimum cost shipping routes for the companyusing stepping stone
method.
(b) The Adams Fruit Company management has negotiated a newshipping contract with a
trucking firm between its Sargodha farm and its distributor inKarachi that reduces the
shipping cost per ton from $0.80 per ton to $0.55 per ton. How willthis cost change
affect the optimal solution?
(c) Sometimes one or more of the routes in the transportation modelare prohibited. That is,
units cannot be transported from a particular source to aparticular destination. Because of
an agreement between distributors, shipments are prohibited fromSargodha to Quetta.
Shipments are also prohibited from Sahiwal to Lahore because ofrailroad construction,
what will be the effect on the optimal shipping routes? Solve thisproblem