MATH 1325 Lab 3 - Part B: Applications of the Derivative

Instructions: Show all work and write your solution to the problems neatly on this handout. Box your final answer. If you need help, feel free to consult with your professor or go to the Math Lab for assistance.

1. Let x represent the units of labor and y the capital invested in a manufacturing process. When

135,540 units are produced, the relationship between labor and capital can be modeled by

100x0.75 y0.25 = 135.540.

a. Find the rate of change of capital with respect to units of labor ) when labor is 1500 units and

the capital invested is 1000 units. Use implicit differentiation.

b. As more labor is used, what happens to the available capital? Write your answer in a complete

sentence

c. As more capital is used, what happens to the available labor? Write your answer in a complete

sentence