Determine an initial basic feasible solution to the following transportation problem by using (a) the least cost method, and (b) Vogels approximation method. Based on the initial basic feasible solution, apply Modified Distribution method (MODI) to determine the optimum cost to the transportation problem (4Points).

Source	Destinations				Supply
	D1	D2	D3	D4
S1	1	2	1	4	30
S2	3	3	2	1	50
S3	4	2	5	9	20
Demand	20	40	30	10

7. DANGOTE Cement factory has divided its sales area in to 3 regions in Africa: East, Midwest, and West. The company has 4 sales representatives who are to be assigned to these 3 regions in a manner that will result in maximum dollar sales. The company will not restrict the number of sales representatives that can be assigned to any one region. The sales return that will be generated in each region from each possible combination of sales representatives are shown in the following table (3Points).

Sales Representatives per region	Return per Region ($ 1,000s)
	East	Midwest	West
0	$0	$0	$0
1	22	17	25
2	51	48	45
3	65	71	58
4	82	90	75

• Determine the optimal number of sales representatives to assign to each region in order to maximize the total sales returns with the use of dynamic programming solution approach