Chapter 8.2, Problem 49E

PROFIT FUNCTIONS The monthly profit (in dollars) of Bond and Barker Department Store depends on the level of inventory x (in thousands of dollars) and the floor space y (in thousands of square feet) available for display of the merchandise, as given by the equation

P(x, y) = −0.02x² − 15y² +xy + 39x + 25y – 20,000

Compute $\frac{\partial P}{\partial x}$ and $\frac{\partial p}{\partial y}$ when x = 4000 and y = 150. Interpret your results. Repeat with x = 5000 and y = 150.