The maximum value of P = x + 6y subject to the constraints is 9
How to determine the maximum value?
The objective function is given as:
P = x + 6y
The constraints are given as:
2x + 4y ≤ 10
x + 9y ≤ 12
x≥0 y≥0
Rewrite 2x + 4y ≤ 10 and x + 9y ≤ 12 as equations
2x + 4y = 10
x + 9y = 12
Divide 2x + 4y = 10 through by 2
x + 2y = 5
Subtract x + 2y = 5 from x + 9y = 12
x - x + 9y - 2y = 12 - 5
Evaluate the difference
7y = 7
Divide by 7
y = 1
Substitute y = 1 in x + 2y = 5
x + 2(1) = 5
Solve for x
x = 3
So, we have
(x, y) = (3, 1)
Substitute (x, y) = (3, 1) in P = x + 6y
P = 3 + 6 * 1
Evaluate
P = 9
Hence, the maximum value of P = x + 6y subject to the constraints is 9
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