Final answer:
To maximize his profit, the farmer needs to determine how many acres of Crop A and Crop B to plant. Using linear programming, we can solve for the optimal solution that maximizes the objective function P = 180x + 200y, subject to the given constraints. The solution will give us the number of acres for each crop that maximizes the farmer's profit.
Step-by-step explanation:
To maximize his profit, the farmer needs to determine how many acres of each crop to plant. Let's denote the number of acres of Crop A as 'x' and the number of acres of Crop B as 'y'. Since the farmer wants to cultivate at least 80 acres of Crop A, we have the constraint x ≥ 80. The total number of acres available for cultivation is 150, so another constraint is x + y ≤ 150. The total cost of cultivating Crop A is $40/acre and the total cost of cultivating Crop B is $60/acre.
The farmer has a maximum of $7400 available for land cultivation, so the cost constraint is 40x + 60y ≤ 7400. Each acre of Crop A requires 20 labor-hours and each acre of Crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available, so the labor-hours constraint is 20x + 25y ≤ 3300.
Finally, the profit per acre for Crop A is $180 and for Crop B is $200.
To solve this problem, we can use linear programming. We want to maximize the objective function P = 180x + 200y, subject to the constraints mentioned above. The solution to this problem will give us the number of acres of each crop that will maximize the farmer's profit.