Homework SourseA farmeer has 500 acres of land and wishes to determine the
A farmeer has 500 acres of land and wishes to determine the acreage to the following three crops: wheat,corn,soy beans.The man days required ,preperation cost, and profit per acre of the three crops are summarized blow.Suppose that the maximum number of man days available are 5,000 and that the farmer has 70,000 for preperation.
formulate a linear programm that maximizes the farmers profit?
i want variables,constrains and optimal solution linear program
| crop | man days | preperaion cost($) | profits($/acre) |
| wheat | 6 | 100 | 60 |
| corn | 10 | 150 | 90 |
| soy beans | 8 | 120 | 80 |
Solution
Decision Variables:
Let X1 and X2 and X3 be number acres the farmer grows wheat, corn and soy beans respectively.
The objective of the given problem is to maximize the profit.
Profit Z = 60X1 + 90X2 + 80X3
Therefore the objective function is Maximise Z = 60X1 + 90X2 + 80X3
The above objective function is subjected to following constraints.
Since the total area of the firm is 500 acres X1 + X2 + X3 <= 500
The total man-days labour is 5000 man-days
6X1 + 10X2 + 8 X3 <= 5000
Total preparartion cost
100X1 + 150X2 + 120X3 <= 7000
OPTIMAL SOLUTION Z = 60X1 + 90X2 + 80X3
with constraints:X1 + X2 + X3 <= 500 , 6X1 + 10X2 + 8 X3 <= 5000, 100X1 + 150X2 + 120X3 <= 7000
X1, X2, X3 >0
