Four bakeries, \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D , supply bread to four supermarkets, \(\mathrm { P } , \mathrm { Q } , \mathrm { R }\) and S . The table gives the cost, in pounds, of transporting one lorry load of bread from each bakery to each supermarket. It also shows the number of lorry loads of bread at each bakery and the number of lorry loads of bread required at each supermarket. The total cost of transportation is to be minimised.
P
Q
R
S
Supply
A
28
32
33
27
13
B
31
29
26
31
4
C
30
26
29
32
12
D
25
30
28
34
11
Demand
11
10
11
8
Use the north-west corner method to obtain a possible solution.
A partly completed table of improvement indices is given in Table 1 in the answer book.
Complete Table 1.
Taking the most negative improvement index to indicate the entering cell, use the steppingstone method once to obtain an improved solution. You must make your route clear and state your entering cell and exiting cell.