Solve the problem.
-A rock group is producing a new $C D$. The cost in dollars to produce a $C D$ is given by $C(x, y)=21,500+x^{2}-180 x+3 y^{2}-108 y$, where $x$ is the number of man hours of work required and $y$ is the number of hours of studio time required. Find the value of $x$ and the value of $y$ that minimize the cost.
A) 89 man hours of work; 14 hours of studio time
B) 90 man hours of work; 18 hours of studio time
C) 92 man hours of work; 15 hours of studio time
D) 95 man hours of work; 20 hours of studio time

Question

Quizplus · Accepted Answer

The cost function $C(x, y)$ is minimized by finding the critical points using partial derivatives. Setting $\frac{\partial C}{\partial x} = 2x - 180 = 0$ gives $x = 90$, and $\frac{\partial C}{\partial y} = 6y - 108 = 0$ gives $y = 18$.

Solve the Problem CDC DCD the Cost in Dollars to Produce A a New

Solve the Problem $C D$ the Cost in Dollars to Produce A a New