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

• A. $\frac{235}{19}$
• B. $\frac{325}{19}$
• C. $\frac{523}{19}$
• D. $\frac{532}{19}$

Answer 1

Answer: (A)

Given, inequalities are $3x+5y\le 15,5x+2y\le 10,x,y\ge 0$

Also, given $z=5x+3y$
At point $A\left(2,0\right)$
$z=5\times 2+0=10$
At point $B\left(\frac{20}{19},\frac{45}{19}\right)$,
$z=\frac{5\times 20}{19}+\frac{3\times 45}{19}=\frac{235}{19}$
At point $C\left(0,3\right)$
$z=5\left(0\right)+3\times 3=9$
Hence, maximum value of z is $\frac{235}{19}.$