Question

A. An Electrical Company has three workshops in Koforidua, Accra
and Kumasi. These workshops produce the following quantities of
electric fan.
Workshops Monthly production (units)
Koforidua 130
Accra 70
Kumasi 100
The monthly demand for these fans in three towns: Sunyani, Cape
Coast and Ho is given below:
Destination Weekly Demand (units)
Sunyani 80
Cape Coast 110
Ho 60

The unit transportation costs per unit (in GH¢000) from the sources to
the destinations are as shown:
From
To
Sunyani Cape Coast Ho
Koforidua 9 14 12
Accra 11 10 6
Kumasi 12 8 15
(i) Using practical examples from the field of business compare and
contrast the concept of balance and unbalance transportation
problem. Illustrate your understanding of these concepts by
discussing and explaining possible four reasons for balance
or unbalance transportation problem using a practical case in
industry.
(ii)Formulate a linear programming (LP) model.

B.The model in (A) was solved using Solver and part of the Solver
output is shown below. Use it to answer the questions that
follow.
Adjustable Cells
Cell    Name        OriginalValue    Final Value
$C$4 Koforidua Sunyani      80         80
$D$4 Koforidua Cape Coast. 0         0
$E$4 Koforidua Ho                   0.        0
$C$5 Accra Sunyani                 0         0
$D$5 Accra Cape Coast           10      10
$E$5 Accra Ho                           60      60
$C$6 Kumasi Sunyani.              0         0
$D$6 Kumasi Cape Coast         100 100
$E$6 Kumasi Ho.                          0.      0

(i). As a management, science student the MD of the company seeks
your expert advice on ways in which to determine the optimal
transportation rule. Advise the MD, providing detailed explanation
using the table above. Write your answer in a form of a report to the
MD.

Answer 1

Solution ::

(i)

LP model is formulated as below:

Let Xij be the number of units to be transported from source i to destination j

Min 9X11+14X12+12X13+11X21+10X22+6X23+12X31+8X32+15X33

s.t.

X11+X12+X13 <= 130

X21+X22+X23 <= 70

X31+X32+X33 <= 100

X11+X21+X31 = 80

X12+X22+X32 = 110

X13+X23+X33 = 60

Xij >= 0

-------------------------------

(ii)

As per Solution output,

80 units should be shipped from Koforidua to Sunyani

10 units should be shipped from Accra to Cape Coast

60 units should be shipped from Accra to Ho

100 units should be shipped from Kumasi to Cape Coast

Total transportation cost = 80*9+10*10+60*6+100*8

= 1980

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