Linear Programming Question 132
Question: The Maximum value of $ z=5x+3y $ , subjected to the conditions $ 3x+5y\le 15,5x+2y\le 10,x,y\ge 0 $ is
Options:
A) $ \frac{235}{19} $
B) $ \frac{325}{19} $
C) $ \frac{523}{19} $
D) $ \frac{532}{19} $
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Answer:
Correct Answer: A
Solution:
Given, inequalities are $ 3x+5y\le 15, $
$ 4x+2y\le 10,x,y\ge 0 $
Also, given $ z=5x+3y $
At point A (2, 0) $ z=5\times 2+0=10 $
At Pont $ B( \frac{20}{19},\frac{45}{19} ) $
$ z=\frac{5\times 20}{19}+\frac{3\times 45}{19}=\frac{235}{19} $
At point $ C(0,3) $
$ z=5(0)+3\times 3=9 $
Hence, maximum value of z is $ \frac{235}{19} $ .
BETA
