GOAL PROGRAMMING SOLUTION USING EXCEL SOLVER

Montega is a developing country which has 15,000,000 acres of publicly controlled agricultural land in active use. Its government currently is planning a way to divide this land among three basic crops (labeled 1, 2, and 3) next year. A certain percentage of each of these crops is exported to obtain badly needed foreign capital (dollars), and the rest of each of these crops is used to feed the populace. Raising these crops also provides employment for a significant proportion of the population. Therefore, the main factors to be considered in allocating the land to these crops are (1) the amount of foreign capital generated, (2) the number of citizens fed, and (3) the number of citizens employed in raising these crops. The following table shows how much each 1,000 acres of each crop contributes toward these factors, and the last column gives the goal established by the government for each of these factors. Contribution per 1,000 Acres Factor Foreign capital Citizens fed Citizens employed Crop: 1 2 3 Goal $3,000 $5,000 $4,000 $70,000,000 150 75 100 1,750,000 10 15 12 = 200,000 In evaluating the relative seriousness of not achieving these goals, the government has concluded that the following deviations from the goals should be considered equally undesirable: (1) each $100 under the foreign-capital goal, (2) each person under the citizens-fed goal, and (3) each deviation of one (in either direction) from the citizens-employed goal. Formulate a goal programming model for this problem. Montega is a developing country which has 15,000,000 acres of publicly controlled agricultural land in active use. Its government currently is planning a way to divide this land among three basic crops (labeled 1, 2, and 3) next year. A certain percentage of each of these crops is exported to obtain badly needed foreign capital (dollars), and the rest of each of these crops is used to feed the populace. Raising these crops also provides employment for a significant proportion of the population. Therefore, the main factors to be considered in allocating the land to these crops are (1) the amount of foreign capital generated, (2) the number of citizens fed, and (3) the number of citizens employed in raising these crops. The following table shows how much each 1,000 acres of each crop contributes toward these factors, and the last column gives the goal established by the government for each of these factors. Contribution per 1,000 Acres Factor Foreign capital Citizens fed Citizens employed Crop: 1 2 3 Goal $3,000 $5,000 $4,000 $70,000,000 150 75 100 1,750,000 10 15 12 = 200,000 In evaluating the relative seriousness of not achieving these goals, the government has concluded that the following deviations from the goals should be considered equally undesirable: (1) each $100 under the foreign-capital goal, (2) each person under the citizens-fed goal, and (3) each deviation of one (in either direction) from the citizens-employed goal. Formulate a goal programming model for this