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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 − 14y2 + xy + 34x + 37y − 20,000 Compute  ∂P ∂x and  ∂P ∂y when  x = 4000  and  y = 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. Compute  ∂P ∂x and  ∂P ∂y when  x = 5000  and  y = 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.

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 − 14y2 + xy + 34x + 37y − 20,000 Compute  ∂P ∂x and  ∂P ∂y when  x = 4000  and  y = 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. Compute  ∂P ∂x and  ∂P ∂y when  x = 5000  and  y = 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.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.4: Solving Quadratic Equations
Problem 93E
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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 − 14y2 + xy + 34x + 37y − 20,000
Compute 
∂P
∂x
 and 
∂P
∂y
 when 
x = 4000
 and 
y = 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.
Compute 
∂P
∂x
 and 
∂P
∂y
 when 
x = 5000
 and 
y = 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.
 
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 – 14y2 + xy + 34x + 37y – 20,000 ӘР Compute ӘР and when x = 4000 and y 150. ay ӘР -(4000, 150) ax ӘР -(4000, 150) ду Interpret your results. ӘР (4000, 150) tells us that monthly profit increases by $ ax ӘР per thousand dollars increase in inventory. With the same inventory and floor space as above, -(4000, 150) tells us that ду monthly profit decreases by $ per thousand-square-foot increase in floor space. ӘР Compute ӘР and when x = 5000 and y = 150. ду ӘР -(5000, 150) ax ӘР -(5000, 150) ду Interpret your results. ӘР -(5000, 150) tells us that monthly profit decreases by $ ax ӘР -(5000, 150) tells us that ду per thousand dollars increase in inventory. With the same inventory and floor space as above, monthly profit increases by $ per thousand-square-foot increase in floor space. Need Help? Read It Watch It
Transcribed Image Text: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 – 14y2 + xy + 34x + 37y – 20,000 ӘР Compute ӘР and when x = 4000 and y 150. ay ӘР -(4000, 150) ax ӘР -(4000, 150) ду Interpret your results. ӘР (4000, 150) tells us that monthly profit increases by $ ax ӘР per thousand dollars increase in inventory. With the same inventory and floor space as above, -(4000, 150) tells us that ду monthly profit decreases by $ per thousand-square-foot increase in floor space. ӘР Compute ӘР and when x = 5000 and y = 150. ду ӘР -(5000, 150) ax ӘР -(5000, 150) ду Interpret your results. ӘР -(5000, 150) tells us that monthly profit decreases by $ ax ӘР -(5000, 150) tells us that ду per thousand dollars increase in inventory. With the same inventory and floor space as above, monthly profit increases by $ per thousand-square-foot increase in floor space. Need Help? Read It Watch It
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