Question
(a) A plastics manufacturer has 1200 boxes of transparent wrap in stock at one factory and another 1000 boxes at its second factory. The manufacturer has orders for this product from three different retailers, in quantities of 1000, 700 and 500 boxes, respectively. The unit shipping costs (in cents per box) from the factories to the retailers are as follows:

Retailer 1

Retailer 2

Retailer 3

Factory 1

14

13

11

Factory 2

13

13

12

The manufacturer wishes to find the allocation that will involve the minimum total transportation cost.
(1) Use Vogel's Approximation method to obtain an initial basic feasible solution to the above problem.
(2) Hence, use the transportation technique to find the allocation that will involve the minimum total transportation cost.
(b) A company has one surplus truck in each of the cities A, B, C, D and E and one deficit truck in each of the cities 1, 2, 3, 4, 5 and 6. The distances between the cities in kilometres are shown in the table given on

City 1

City 2

City 3

City 4

City 5

City 6

City A

12

10

15

22

18

8

City B

10

18

25

15

16

12

City C

11

10

3

8

5

9

City D

6

14

10

13

13

12

City E

8

12

11

7

13

10


Find the assignment of trucks from cities in surplus to cities in deficit so that the total distance covered by the vehicles is minimum.