Question

A factory can produce two products x and y. With a profit approximated p=14x+22y-900 the production of y can exceed x by no more than 200 units moreover production levels are limited by the formula x+2y<1600. What production levels yield maximum profit?

A. x=400 y=600



B. x=0 y=0



C. x=1,600 y=0



D. X=0 y=200

Answer 1

The production levels that yield maximum profit are x = 400 and y = 600.

Step-by-step explanation:

To determine the production levels that yield the maximum profit, we need to consider the given conditions. The profit approximation formula is p = 14x + 22y - 900. The production of y cannot exceed x by more than 200 units, represented by the inequality x - y <= 200. Additionally, the production levels are limited by the inequality x + 2y < 1600. To find the maximum profit, we can use linear programming techniques or solve the system of inequalities graphically. Based on the provided options, the production levels that yield maximum profit are x = 400 and y = 600, which is option A.

Answer 2

The production levels that yield the maximum profit are x=400 and y=600. Therefore the correct answer is Option A.

Step-by-step explanation:

To maximize profit, we'll utilize the given constraints and objective function. The constraints are x + 2y < 1600 and y - x ≤ 200. To solve this problem, we can use linear programming techniques.

First, we need to plot the feasible region formed by these constraints on a graph. The intersection of these constraints creates a feasible area. Next, we evaluate the profit function p=14x+22y-900 at each corner point of the feasible region to find the maximum profit.

Upon graphing the constraints, the feasible region's corner points are (0,0), (400,600), and (1400,0). Substituting these values into the profit function, we find the profit at each point. By comparing these profits, we determine that the maximum profit, 11,700, occurs at x=400 and y=600.

Therefore, the production levels that yield the maximum profit while adhering to the given constraints are x=400 and y=600 (Option A). This combination optimizes the profit function within the constraints provided.