Four factories, A, B, C and D produce sugar and the capacity of each factory is given below: Factory A produces 10 tons of sugar and B produces 8 tons of sugar, C produces 5 tons of sugar and that of D is 6 tons of sugar. The sugar has demand in three markets X, Y and Z. The demand of market X is 7 tons, that of market Y is 12 tons and the demand of market Z is 4 tons. The following matrix gives the transportation cost of 1 ton of sugar from each factory to the destinations.
  Find the Optimal Solution for least transportation cost

Factories. A B C D Requirement in tons. X 4 5 6 3 7 Cost in Rs. per ton (x 100) Markets. Y 3 6 4 5 12 Z 2 1 3 4 4 Availability in tons. 10 8 5 6 _b = 29, _d=23