This document presents a linear transportation problem to minimize transportation costs from three origin factories (Ondo, Osun, Oyo) with certain capacities to four destination depots (Abuja, Lagos, Kano, Enugu) with requirements, given the transportation costs between each origin-destination pair. The optimal solution assigns shipments from each origin to meet all destination requirements at minimum total cost of 1 billion NGN.

1. Transportation Problem
Abuja Lagos Kano Enugu Origin
Capacity(tonnes)
Ondo 6,000
Osun 1,000
Oyo 10,000
Destination
Requirement(tonnes)
7,000 5,000 3,000 2,000
Transportation Costs
Abuja Lagos Kano Enugu
Ondo 20 30 110 70
Osun 10 00 60 10
Oyo 50 80 150 90
Costs are in ‘000 NGN.
Linear problem formulation
Min: 20x1+30x2+110x3+70x4+10x5+0x6+60x7+10x8+50x9+80x10+150x11+90x12 #the problem is to
minimize the costs of transportation from the processing factories/ plants to the various depots
Subject to
X1+X2+X3+X4<=6,000 #ondo factory capacity. The maximum that the Ondo plant can supply
X5+X6+X7+X8<=1,000 #osun factory capacity. Maximum supply of the Osun plant
X9+X10+X11+X12<= 10,000 #oyo factory capacity. Maximum supply of the Oyo plant
X1+X5+X9 >=7,000 #abuja depot requirement. Minimum to satisfy the demand at the Abuja depot
X2+X6+X10>= 5,000 #lagos depot requirement. Minimum to satisfy the demand at the Lagos depot
X3+X7+X10>= 3,000 #kano depot requirement. Minimum to satisfy the demand at the Lagos depot
X4+X8+X12>= 2,000 #enugu depot requirement. Minimum to satisfy the demand at the Lagos depot
Optimum Solution
Abuja Lagos Kano Enugu
Ondo 5000 1000 6,000
Osun 1000 1,000
Oyo 7000 1000 2000 10,000
7,000 5,000 3,000 2,000
Total Minimum Cost = N 1billion