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Chap 8 WE

# Chap 8 WE - Worked Examples for Chapter 8 Example for...

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Worked Examples for Chapter 8 Example for Section 8.1 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. Let England, France, and Spain be the three sources, where their supplies are the millions of acres of land that are available for growing these crops. Let Wheat, Barley, and Oats be the three destinations, where their demands are the millions of acres of land that are needed to fulfill the world demand for these respective crops. The unit cost (in millions of dollars) is the labor cost per million acres, so the number of hours of labor needed is multiplied by the cost per hour. The parameter table is as follows. Unit Cost (\$ million) Destination Wheat Barley Oats Supply

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England 162 121.5 82.8 70 Source France 93.6 108 75 110 Spain 158.4 100.8 100.8 80 Demand 125 60 75
(b) Draw the network representation of this problem. The network presentation of this problem is given below. (c) Obtain an optimal solution. We can use the Excel Solver to solve this problem and obtain the following solution. Allocation Quantities

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Chap 8 WE - Worked Examples for Chapter 8 Example for...

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