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Given the constraints below, which vertex maximizes the linear function $f(x)=5x+6y$?

$y\leq3$
$x\leq4$
$y\leq-\cfrac{1}{2}x+4$

A

$(0,3)$

B

$(2,3)$

C

$(4,2)$

D

$(4,0)$

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