1. Suppose that England, France, and Spain produce all the wheat, barley, and oats in the world. The world demand for wheat requires 125 million acres of land devoted to wheat production. Similarly, 60 million acres of land are required for barley and 75 million acres of land for oats. The total amount of land available for these purposes in England, France, and Spain is 70 million acres, 110 million acres, and 80 million acres, respectively. The number of hours of labor needed in England, France and Spain to produce an acre of wheat is 18, 13, and 16, respectively. The number of hours of labor needed in England, France, and Spain to produce an acre of barley is 15, 12, and 12, respectively. The number of hours of labor needed in England, France, and Spain to produce an acre of oats is 12, 10, and 16, respectively. The labor cost per hour in producing wheat is $9.00, $7.20, and $9.90 in England, France, and Spain, respectively.
The labor cost per hour in producing barley is $8.10, $9.00, and $8.40 in England, France, and Spain respectively. The labor cost per hour in producing oats is $6.90, $7.50, and $6.30 in England, France, and Spain, respectively. The problem is to allocate land use in each country so as to meet the world food requirement and minimize the total labor cost.
(a) Formulate this problem as a transportation problem by constructing the appropriate parameter table.
(b) Draw the network representation of this problem.
(c) Obtain an optimal solution.
2. Reconsider the problem in the preceding example. Starting with the northwest corner rule, interactively apply the transportation simplex method to obtain an optimal solution for this problem.