The maximum profit can be achieved by finding the vertex of the feasible region defined by the production limits.
First, let's consider the production limits:
1) Production of y can exceed × by no more than 200 units.
This constraint can be represented as y - x ≤ 200.
2) Production levels are limited by the formula ×+2y<1600.
This constraint can be represented as x + 2y ≤ 1600.
Now, let's plot these constraints on a graph:
To plot the constraint y - x ≤ 200, we can rewrite it as x = y - 200.
To plot the constraint x + 2y ≤ 1600, we can rewrite it as y = (1600 - x)/2.
Here is the graph:
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y
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0 x
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To find the maximum profit, we need to find the vertex of the feasible region. This can be done by evaluating the profit function P at the vertices of the feasible region.
The vertices of the feasible region are:
A: x = 0, y = 0
B: x = 0, y = 200
C: x = 400, y = 600
D: x = 1200, y = 200
Evaluating the profit function P at each vertex gives us the following profits:
A: P = 14(0) + 22(0) - 900 = -900
B: P = 14(0) + 22(200) - 900 = 1300
C: P = 14(400) + 22(600) - 900 = 22100
D: P = 14(1200) + 22(200) - 900 = 26600
Therefore, the production levels that yield maximum profit are:
x = 1200 and y = 200.
A 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?
×=400; y=600
×=0; y=0
×=1,600; y=0
×=0; y=200
1 answer