Chapter 4.6, Problem 54E

Productivity The number of cellphone accessory kits (neon lights, matching covers, and earbuds) per day that USA Cellular Makeover, Inc., can manufacture at its plant in Cambodia is given by

$P=x^{0.5}{y}^{0.5},$

Where x is the number of workers at the plant and y is the monthly budget (in dollars). Assume that P is constant, and compute $\frac{dy}{dx}$

when $x=200\text{ and }y=100,000$, Interpret the result. [HINT: See Example 5.]