Question

suppose the quantity demanded per week of a certain dress is related to the unit price p by the demand equation p=sqrt800-x. write the function that describes the revenue function? To maximize revenue how many dresses should be made and sold each week?

Answer 1

p = √(800-x)
revenue is quantity * price, so
r = x√(800-x)
dr/dt = (1600-3x) / 2√(800-x)
dr/dt=0 when 1600-3x=0, or x=1600/3

a bit of further analysis will show that this is a max, not a min.

Answer 2

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