Question

A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y - 900. The production of y must exceed the production of x by at least 100 units. Moreover, production levels are limited by the formula x + 2y ≤ 1400. Identify the vertices of the feasible region. What production levels yield the maximum profit, and what is the maximum profit?

a. Vertices: (0, 0), (600, 1000), (700, 1000), Maximum Profit: $13,000
b. Vertices: (0, 0), (300, 400), (700, 1000), Maximum Profit: $13,000
c. Vertices: (0, 0), (500, 800), (700, 1000), Maximum Profit: $12,700
d. Vertices: (0, 0), (400, 500), (700, 1000), Maximum Profit: $11,800

Answer 1

The vertices of the feasible region are (0, 0), (600, 1000), and (700, 1000). The production levels that yield the maximum profit are (600, 1000), with a maximum profit of $13,000.

Step-by-step explanation:

The vertices of the feasible region are (0, 0), (600, 1000), and (700, 1000). These points satisfy the constraint x + 2y ≤ 1400. To find the production levels that yield the maximum profit, we need to evaluate the profit function at each of the vertices. By substituting the x and y values of each vertex into the profit function P = 14x + 22y - 900, we find that the maximum profit is $13,000, which occurs at the vertex (600, 1000).