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 below.

Question

P(x, y) = -0.016x^2 - 17y^2 + xy + 28x + 22y - 20000
(a) Compute Px and Py when x = 4000 and y = 150.
Px = ?
Py = ?

(b) Repeat with x = 5000 and y = 150.
Px = ?
Py = ?
NOTE: I do not know how to do it. It will help if you show step by step. Thanks

Answer 1

a)
dp/dx = -.032x + y + 28

= -.032(4000) + 150(1) + 28
= -128 + 150 + 28
= 50

dp/dy = -34y + x + 22

= -34(150) + 4000(1) + 22
= -5100 + 4000+ 22
= -1078

b)
dp/dx = -.032x + y + 28
= -.032(5000) + 150(1) + 28
= -160 + 150 + 28
= 18

dp/dy = -34y + x + 22
= -34(150) + 5000(1) + 22
= -5100 + 5000 + 22
= -78