Question A factory can produce two products, x and y, with a profit approximated by 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? (1 point) Responses x = 400; y = 600 x = 400; y = 600 x = 0; y = 0 x = 0; y = 0 x = 1,600; y = 0 x = 1,600; y = 0 x = 0; y = 200
To find the production levels that yield maximum profit, we need to analyze the given constraints.
First, let's consider the production constraint: x + 2y ≤ 1600. This means that the production levels of x and y must fall within this limit.
Next, we have the constraint that the production of y can exceed x by no more than 200 units: y ≤ x + 200.
Given these constraints, we can test each given response to see which combination of x and y satisfies both constraints and maximizes profit.
1. x = 400; y = 600
Plugging these values into the constraints:
400 + 2(600) = 1600 ≤ 1600 (satisfied)
600 ≤ 400 + 200 (satisfied)
2. x = 0; y = 0
Plugging these values into the constraints:
0 + 2(0) = 0 ≤ 1600 (satisfied)
0 ≤ 0 + 200 (satisfied)
3. x = 1600; y = 0
Plugging these values into the constraints:
1600 + 2(0) = 1600 ≤ 1600 (satisfied)
0 ≤ 1600 + 200 (not satisfied)
Therefore, the production levels that yield the maximum profit are x = 400 and y = 600.