to increase revenue, a sports store has decided to increase the cost of a baseball glove. they expect that for every 5$ increase in price from the current price of 40$, three fewer gloves will be sold per week than the current 60 per week. what is the selling price that will maximize the revenue and what is the maximum revenue?

Question

to increase revenue, a sports store has decided to increase the cost of a baseball glove. they expect that for every 5$ increase in price from the current price of 40$, three fewer gloves will be sold per week than the current 60 per week. what is the selling price that will maximize the revenue and what is the maximum revenue?

Answer 1

revenue = (40 + 5 x) (60 - 3 x) = 2400 + 180 x - 15 x^2

the max is on the axis of symmetry of the parabola
... xmax = -b / (2 a) = -180 / -30 = 6

substitute into the revenue equation to find the max price and revenue