Question

A farmer plans to plant two crops, A and B. The cost of cultivating Crop A is $40/acre whereas the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. 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. If she expects to make a profit of $170/acre on Crop A and $210/acre on Crop B, how many acres of each crop, x and y, respectively, should she plant in order to maximize her profit?

Answer 1

The question requires solving a linear programming problem to maximize profit for a farmer planting two crops within budget and labor constraints. The objective function is P = 170x + 210y, and the constraints include budget and labor-hours. Graphical methods or the simplex algorithm are used for finding the optimal solution.

Step-by-step explanation:

The question involves a linear programming problem where a farmer is trying to maximize profit by planting two types of crops, A and B, subject to constraints on budget and labor hours. The farmer's problem can be set up with two variables, x for acres of Crop A and y for acres of Crop B. The objective function, representing total profit, is P = 170x + 210y, which needs to be maximized.

The constraints for the problem, based on the budget and labor hours available, are:

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To solve this, one would typically use graphical methods or the simplex algorithm to find the combination of x and y that maximizes P while satisfying all constraints.