general contractor A who is engaged in the construction of civil works has
got projects at four different parts of Ethiopia that require cement for the
execution of the projects. The cement required for these projects are obtained
from the three factories located at different parts of the country. The demand
of OPC cement for each project site is 1100 qtls 1200qtls 800qtls and 1400
qtls for projects 1 to 4 respectively. The contractor is able to obtain 2000
qtls 1500 qtls and 1000 qtls of OPC cement from factories of F1 to F3
respectively.Table 2: Distance of project sites from factoriesNB:
A-Asphalt Road Length in km G-Gravel Road Length in kmFactoriesP1P2P3P4F1A600A800A900A700G400G400G600G300F2A200A200A200A100G300G400G500G300F3A500A1000A450A700G300G300G450G400The unit
cost of OPC cement at the three factories is equal. However; transportation
on the distance and road condition. The distance of the factories from each
Kilometer is shown in table 2. The length of each road is divided into its
asphalt and gravelcomponent.The
unit transportation cost of cement is 10 cents/qtl*Km for gravel road and 5
asphalt roadFrom the above
Calculate the unit transportation cost of cement
to each project sites from the factories and find the starting feasible
solution with the use of Matrix minima methodb.
Find the least total transportation cost of the
contractor that he should spend in transporting cements from factories to all
his project sites.c.
If the transporters have decided to change the
unit transportation cost of cement at F1 and F2 by 5 % and 3 % more than that of F3 respectively show the allocated quantities of
cement to each project that minimizes the total project cost.