Three wells in different oil fields (w1, w2 and w3) with production capacity of (seven, eighteen, nine) tons per hour, respectively. These tons are to be shipped to (4) destinations (A1, A2, A3 and A4) with requirement of (five, six, seven, fourteen) tons per hour respectively. The costs of transportation per ton between wells and destinations are given in the following table.

Find the initial basic feasible solution to the transportation problem, use the Vogle`s approximation method and then complete the solution by applying the modified distribution method to obtain the optimal solution.

Ai A2 A3 A4 W1 19 30 50 10 W2 70 30 40 60 W3 40 8 70 20