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The firm XYZ produces certain agricultural products such as sugar beet, wheat, and cotton. There are three different arable lands in the region. The table below represents the maximum arable land in acre and available water resource in m3.
Land
Maximum arable land (acres)
Maximum available water (m3)
Land 1
500
900
Land 2
700
1000
Land 3
800
1200
The following table shows the maximum quota in acres, unit water consumption and unit profit per acres of each product.
Product
Maximum quota (acres)
Water consumption (m3/Acre)
Profit ($/Acre)
Sugar beet
750
5
1450
Cotton
850
3
1350
Wheat
950
2
1250
The management of the XYZ firm would like to determine how many acres of each product should be planted in each land to maximize the total profit.
a) Define the decision variables,
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