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Optimizing
A light is suspended at a height h above the floor (see figure below). The illumination at the point P is inversely proportional to the square of the distance from the point P to the light and directly proportional to the cosine of the angle θ. Let d = 2 ft.
(a) Express the illumination in terms of h only. Use k for the proportionality constant.
(b) How far from the floor should the light be to maximize the illumination at the point P? (in ft)
I am not sure how to approach this problem, I think I am missing something. Attached is a photo of what the problem looks like.