Profit FunctionsThe monthly profit (in dollars) of Bond and Barker Department Store depends on the level of inventoryx(in thousands of dollars) and the floor spacey(in thousands of square feet) available for display of the merchandise, as given by the equation.

P(x,y) =0.02x²14y²+xy+26x+35y20,000

ComputeP/x andP/y whenx= 4000 andy= 150.

P/x (4000, 150)=

P/y(4000, 150)=

Interpret your results.

P/x (4000, 150)

tells us that monthly profit increases by$per thousand dollars increase in inventory. With the same inventory and floor space as above,P/y

(4000, 150)tells us that monthly profit decreases by$per thousand-square-foot increase in floor space.

ComputeP/x

andP/y whenx= 5000andy= 150.

P/x(5000, 150)=P/y(5000, 150)=

Interpret your results.

P/x(5000, 150)tells us that monthly profit decreases by$per thousand dollars increase in inventory. With the same inventory and floor space as above,P/y (5000, 150)tells us that monthly profit increases by$per thousand-square-foot increase in floor space.