The profit generated by an information technology consulting firm can be modeled as
$P(x, y) = -4x^2 + 96x + 168y - 7y^2$ millon dollars
where x thousand hours are logged by on-site desktop engineers and y thousand hours are logged by network systems engineers.
(a) Calculate the point of maximized profit.
x =
y =
thousand hours
thousand hours
(b) Verify that the result of part (a) is a maximum point.
Find the second partials.
$P_{xx} = $
$P_{yy} = $
$P_{xy} = $
$P_{yx} = $
Using the Determinant Test, $D(x, y) = $
Since D ? 0 and $P_{xx}$ ? 0, the critical point is a relative maximum.
