a) Engineering Works Ltd has a network of branches all over Kenya .The branches are used to service repair and install equipment for their clients .Currently, the Nairobi branch has four clients who require installation of equipment .Each client requires the services of one engineer. There are four engineers who are not engaged at the moment and can be assigned any one of the tasks .However, these engineers have to travel form different locations and the Nairobi branch has to meet their travel and subsistence allowances. The allowances vary from one engineer to another and according to the client the engineer has been assigned to work for.

The table below shows the costs (in thousands of shillings) associated with each engineer

Client

Engineers	1	2	3	4
A	37.0	27.0	34.0	21.0
B	57.0	22.0	79.0	34.0
C	22.0	25.0	61.0	45.0
D	39.0	42.0	54.0	43.0

Required

Assign engineers to clients order to minimize their total cost

Solve the following transportation problem by using:

b) North west corner rule method and Vogel's Approximation method