Question

farmer has 100 acres of land to devote to wheat and corm and wishes to plan his crops in order to maximize his revenue. He has only $800 in capital allocated for planting the crops. It costs $5 to plant an acre of wheat and $10 for an acre of corn. His other activities leave his family only 150 days of labour to devote to the crops. Two days are required for each acre of wheat and one day for an acre of corn. Past experience indicates a return of $80 from each acre of wheat and $60 from each acre of corn. a) Formulate an LP problem that can decide how many acres of each should be planted to maximize his revenue?

Answer 1

To formulate an LP problem that can decide how many acres of each crop the farmer should plant to maximize his revenue, we can use variables for the number of acres of wheat and corn, an objective function to maximize revenue, and constraints for capital and labor. The equations can be used to determine the optimal solution.

Step-by-step explanation:

To formulate an LP problem that can decide how many acres of each crop the farmer should plant to maximize his revenue, we can use the following variables:

• Let x be the number of acres of wheat to be planted
• Let y be the number of acres of corn to be planted

The objective function is to maximize the revenue, which can be expressed as:

R = 80x + 60y
The constraints are:The farmer has only $800 in capital allocated for planting the crops, which can be expressed as:
5x + 10y ≤ 800

The family has only 150 days of labor to devote to the crops, which can be expressed as:

2x + y ≤ 150

The number of acres cannot be negative, which can be expressed as:x ≥ 0, y ≥ 0

These equations can be used to determine the number of acres of each crop the farmer should plant to maximize his revenue.