4. Linear Programming
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We have been given a feasible region with an objective function P=x+2y.
x=10, y=0
Zero Property of Multiplication
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Vertex | Objective Function | P |
---|---|---|
B(10,0) | P=10+2(0) | 10 |
C(10,3) | P=10+2(3) | 16 |
D(4,6) | P=4+2(6) | 16 |
E(0,6) | P=0+2(6) | 12 |
At the points C and D, the value of P is 16 which is maximum. This means that the objective function passes through the points C and D. Therefore, the points on the segment CD, yield the maximum profit. Let's choose two more point on the segment.
Let's check the points!
Vertex | Objective Function | P |
---|---|---|
F(8,4) | P=8+2(4) | 16 |
G(6,5) | P=6+2(5) | 16 |
The points F and G also yield the maximum profit. As a result, we have four points C,D,F,G that yield the maximum profit.