Find the indicated maxima or minima.
-Minimum of $f(x, y)=x^{2}+y^{2}-x y$, subject to $x-y=10$
A) 75 when $x=5, y=-5$
B) 7 when $x=2, y=-1$
C) 3 when $x=1, y=2$
D) 25 when $x=5, y=5$

Question

Quizplus · Accepted Answer

To find the minimum, substitute $y = x - 10$ into $f(x, y)$ to get $f(x, x-10) = x^2 + (x-10)^2 - x(x-10)$. Simplifying gives $f(x, x-10) = 2x^2 - 20x + 100$. The minimum occurs at $x = 5$, giving $y = -5$ and $f(5, -5) = 75$.

Find the Indicated Maxima or Minima f(x,y)=x2+y2−xyf(x, y)=x^{2}+y^{2}-x yf(x,y)=x2+y2−xy , Subject To

Find the Indicated Maxima or Minima $f(x, y)=x^{2}+y^{2}-x y$ , Subject To