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Find the maximum value of
P = x + 6y
subject to the following constraints:
(2x + 4y < 10
X + 9y < 12
x > 0
y0
P = [?]

Sagot :

raphealnwobi

Answer:

(3, 1)

Step-by-step explanation:

Given the following constraints:

2x + 4y ≤ 10

x + 9y ≤ 12

x ≥ 0

y ≥ 0

We have to first graph the above constraints and secondly, we find the  boundary points for the feasible region. This is done by plotting the graphs of 2x + 4y ≤ 10  and x + 9y ≤ 12.

 From the graph, the following points satisfy the constraints:

(0,0) , (3,1) , (0,4/3) , (5,0)

Given that:

P = x + 6y

For (0, 0): P = x + 6y = 0 + 6(0) = 0

For (3, 1): P = x + 6y = 3 + 6(1) = 9

For (0, 4/3) P = x + 6y = 0 + 6(4/3) = 8

For (5, 0) P = x + 6y = 5 + 6(0) = 5

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