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Equation of Perpendicular from a Point on a Line

y≤ -15x + 300...

Question

$y \leq - 15 x + 3000$
$y \leq 5 x$
In the xy-plane, if a point with coordinates $(a, b)$ lies in the solution set of the system of inequalities above, what is the maximum possible value of b?

A

750

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B

600

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C

900

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D

150

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Solution

The correct option is A $750$
The maximum value of b occurs when take equality.
$\Rightarrow - 15 x + 3000 = 5 x$
$\Rightarrow - 20 x = - 3000$
$\Rightarrow - 20 x = - 3000$
$\Rightarrow x = 150$
Therefore , $y = 5 \times 150 = 750$
Hence maximum possible value of $b = 750$

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