To find the production levels that yield the maximum profit, we can use optimization techniques.
First, let's set up the constraints based on the given information. We have two constraints:
1) The production of y can exceed x by no more than 200 units: y - x ≤ 200
2) Production levels are limited by the formula x + 2y < 1600
Now let's analyze the options:
- Option 1: x = 400; y = 600
- Option 2: x = 0; y = 0
- Option 3: x = 1,600; y = 0
- Option 4: x = 0; y = 200
We need to check if these options satisfy the constraints.
- Option 1: (400) + 2(600) = 1600, which satisfies the second constraint. However, y - x = 200, which violates the first constraint.
- Option 2: (0) + 2(0) = 0, which satisfies the second constraint. But y - x = 0 - 0 = 0, which violates the first constraint.
- Option 3: (1600) + 2(0) = 1600, which violates the second constraint.
- Option 4: (0) + 2(200) = 400, which satisfies the second constraint. y - x = 200 - 0 = 200, which satisfies the first constraint.
Only option 4, x = 0; y = 200, satisfies both constraints.
Therefore, the production levels that yield the maximum profit are x = 0 and y = 200.
factory can produce two products x and y with a profit approximated by P=14×+22y-900. The production of y can exceed × by no more than 200 units. Moreover, production levels are limited by the formula ×+2y<1600. What production levels yield maximum profit? Choose from answers.
- ×=400; y=600
- ×=0; y=0
- ×=1,600; y=0
- ×=0; y=200
1 answer