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.

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 = ?

To compute Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.

(a) When x = 4000 and y = 150:
To find Px, we differentiate P(x, y) with respect to x while treating y as a constant.
Differentiating P(x, y) with respect to x, we have:
Px = dP(x, y)/dx = d(-0.016x^2 - 17y^2 + xy + 28x + 22y - 20000)/dx
Simplifying the above equation, we get:
Px = -0.032x + y + 28

To find Py, we differentiate P(x, y) with respect to y while treating x as a constant.
Differentiating P(x, y) with respect to y, we have:
Py = dP(x, y)/dy = d(-0.016x^2 - 17y^2 + xy + 28x + 22y - 20000)/dy
Simplifying the above equation, we get:
Py = -34y + x + 22

Substituting x = 4000 and y = 150 into the above equations:

Px = -0.032(4000) + 150 + 28
= -128 + 150 + 28
= 50

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

Therefore, when x = 4000 and y = 150, Px = 50 and Py = -1078.

(b) When x = 5000 and y = 150:
Using the same process as in part (a), we can find:

Px = -0.032(5000) + 150 + 28
= -160 + 150 + 28
= 18

Py = -34(150) + 5000 + 22
= -5100 + 5000 + 22
= -78

Therefore, when x = 5000 and y = 150, Px = 18 and Py = -78.