MATH 142: Elements of Calculus II
Critical Points of a Function of Two Variables

Work in groups of two to answer the questions below. Put the names of the people in your group at the top of the page and write your answers on the page. You may wish to work the problems on scratch paper before writing your final answer. This will count as one homework assignment.

This project was adapted from question 22 on page 573 of Tan's Calculus For the Managerial, Life and Social Sciences.

Weston Publishing publishes and sells x standard copies of its English-language dictionary and y deluxe editions daily. The daily revenue from this is given by the equation:

R(x,y) = -0.005x2 - 0.003y2 - 0.002xy + 20x + 15y

In dollars, the total daily cost of publishing these dictionaries is:

C(x,y) = 6x + 3y + 200

  1. Find a function P(x,y) that describes Weston Publishing's profit from publishing English-language dictionaries.





  2. Find the critical point(s) of P(x,y).















  3. For each critical point you found, state whether it is a relative maximum of P(x,y), a relative minimum, or neither.






  4. If Weston Publishing asked you how many copies of each dictionary to publish each day what would you advise? Why?