Minimize $S = x + y$ with $x y = 25$ and both $\chi$ and $y 0$ .
A) $S = - 15$
B) $S = 10$
C) $S = 25$
D) $S = 8$
E) $S = 5$

Question

Minimize $S = x + y$ with $x y = 25$ and both $\chi$ and $y > 0$ . 
A) $S = - 15$
B)   $S = 10$
C)   $S = 25$
D)  $S = 8$
E)   $S = 5$

Quizplus · Accepted Answer

Using the constraint $xy = 25$, express $y$ as $y = \frac{25}{x}$. Substitute into $S = x + y$ to get $S = x + \frac{25}{x}$. To minimize $S$, take the derivative $\frac{dS}{dx} = 1 - \frac{25}{x^2}$, set it to zero, and solve for $x$. This gives $x = 5$, and consequently $y = 5$. Thus, $S = 5 + 5 = 10$.

Minimize S=x+yS = x + yS=x+y With xy=25x y = 25xy=25 And Both

Minimize $S = x + y$ With $x y = 25$ And Both