Using the following system of inequalities find the maximum value of f(x,y) = 3x + 7y
1 answer:
X ≥ 0
y ≥ 0
f(x, y) = 3x + 7y
f(0, 0) = 3(0) + 7(0)
f(0, 0) = 0 + 0
f(0, 0) = 0
3x + 2y ≤ 18 ⇒ 3x + 2y = 18 ⇒ 21x + 14y = 126
6x + 7y ≤ 42 ⇒ 6x + 7y = 42 ⇒ <u>12x + 14y = 84</u>
<u>9x</u> = <u>42</u>
9 9
x = 4²/₃
3x + 2y = 18
3(4²/₃) + 2y = 18
14 + 2y = 18
<u>- 14 - 14</u>
<u>2y</u> = <u>4</u>
2 2
y = 2
(x, y) = (4²/₃, 2)
f(x, y) = 3x + 7y
f(4²/₃, 2) = 3(4²/₃) + 7(2)
f(4²/₃, 2) = 14 + 9
f(4²/₃, 2) = 23
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