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,
b) Formulate the LP model of the given problem (objective function and the constraints), and
c) Solve it by the MS Excel Solver.