Question

To prevent pests, an orchard can have no more than 9 times as many apple trees as peach trees. Also, the number of apple trees plus 3 times the number of peach trees must not exceed 348. The revenue from a single apple tree is $124 and the revenue from a single peach tree is $168. Determine the number of each type of tree that will maximize revenue. What is the maximum revenue? Let x represent the number of apple trees and y represent the number of peach trees. Answer 2 Points Кеурас Keyboard Shortcu Enter the value in the first box and the ordered pair in the second box. M

Answer 1

To maximize orchard revenue, we use linear programming to graph constraints x ≤ 9y and x + 3y ≤ 348, and maximize the revenue function R = 124x + 168y by evaluating it at the feasible region's corner points.

Step-by-step explanation:

To maximize revenue for the orchard with constraints on the number of apple trees (x) and peach trees (y), we'll need to set up inequalities and use linear programming. The two constraints are x ≤ 9y (no more than 9 times as many apple trees as peach trees) and x + 3y ≤ 348 (number of apple trees plus 3 times the number of peach trees must not exceed 348). The revenue functions are $124x for apple trees and $168y for peach trees. To find the combination of apple and peach trees that maximizes revenue, we must graph the constraints, identify the feasible region, and evaluate the revenue function at the corner points of this region.

The objective revenue function R = 124x + 168y needs to be maximized. To identify the maximum revenue and the number of each type of tree, the corner points of the feasible region created by the inequalities should be calculated and then substituted into the revenue function. The solution will be the corner point that gives the highest value for R.

Answer 2

To solve the problem, set up a system of inequalities to represent the given conditions and calculate the revenue for each corner point to find the maximum revenue. The detailed calculations are not provided.

Step-by-step explanation:

To solve this problem, we can set up a system of inequalities to represent the given conditions. Let x be the number of apple trees and y be the number of peach trees.

The first condition states that the orchard can have no more than 9 times as many apple trees as peach trees. This can be written as: x ≤ 9y.

The second condition states that the number of apple trees plus 3 times the number of peach trees must not exceed 348. This can be written as: x + 3y ≤ 348.

The objective is to maximize revenue, which can be calculated by multiplying the number of each type of tree by its respective revenue per tree. The revenue from a single apple tree is $124 and the revenue from a single peach tree is $168.

To find the values of x and y that will maximize revenue, we can graph the feasible region formed by the system of inequalities and find the corner point within the region that yields the highest revenue. Calculating the revenue for each corner point will allow us to determine the maximum revenue.

The detailed calculations for finding the corner point and maximum revenue have not been provided, but this is the general approach to solving the problem.