Question

Albert E., a bright elementary school kid and future entrepreneur, is thinking about his lemonade stand at Walmart. In the afternoon at 2 pm his sales of cups of lemonade are falling at 14 per hour. So he decides to raise his price at a rate of $0.05 per hour to compensate. If he has sold 81 cups at 2pm and his price is $0.65 per cup how fast is his revenue changing at 2pm given his new pricing strategy. (assume the changing price doesn't effect quantity sold)

Answer 1

After 2 pm, the price is changing at $0.05/hr
so the price function is p(t) = 0.65 + 0.05t
where t is the number of hours after 2 pm
So the change in revenue has to be adjusted by
81*0.05 = $4.05/hr

Add that to the falling revenue of $14/hr, and the new rate of change of revenue is -$9.95/hr