Solve the problem.
-Suppose that the labor cost for a building is approximated by $C(x, y)=4 x^{2}+3 y^{2}-280 x-240 y+22,000$, where $x$ is the number of days of skilled labor and $y$ is the number of days of semiskilled labor required. Find the $x$ and $y$ that minimize cost $C$.
A) $x=35, y=40$
B) $x=40, y=60$
C) $x=70, y=80$
D) $x=60, y=120$

Question

Quizplus · Accepted Answer

To minimize the cost function $C(x, y)$, we find the critical points by setting the partial derivatives equal to zero. Solving $\frac{\partial C}{\partial x} = 8x - 280 = 0$ gives $x = 35$, and solving $\frac{\partial C}{\partial y} = 6y - 240 = 0$ gives $y = 40$. Thus, the minimum cost occurs at $x = 35$ and $y = 40$.

Solve the Problem C(x,y)=4x2+3y2−280x−240y+22,000C(x, y)=4 x^{2}+3 y^{2}-280 x-240 y+22,000C(x,y)=4x2+3y2−280x−240y+22,000 , Where xxx

Solve the Problem $C(x, y)=4 x^{2}+3 y^{2}-280 x-240 y+22,000$ , Where $x$