## MATH 142: Elements of Calculus II

Critical Points of a Function of Two Variables

Names:

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) = -0.005x*^{2} - 0.003y^{2} - 0.002xy + 20x + 15y
In dollars, the total daily cost of publishing these dictionaries is:

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

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

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

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

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