To find the maximum amount of money made, we need to find the vertex of the revenue equation y = (20 + 0.5x)(1000 - 20x).
First, we need to expand the equation:
y = 20,000 + 500x - 400x - 10x^2
y = -10x^2 + 100x + 20,000
Now, the x-coordinate of the vertex is given by:
x = -b/(2a) = -100/(2*(-10)) = 5
To find the maximum revenue, we substitute x = 5 into the revenue equation:
y = -10(5)^2 + 100(5) + 20,000
y = -250 + 500 + 20,000
y = 20,250
Therefore, the maximum amount of money made is $20,250.
To find the new price that would give the maximum revenue, we substitute x = 5 into the equation for the new price: 20 + 0.5x
new price = 20 + 0.5(5)
new price = 20 + 2.5
new price = $22.50
Therefore, the new price that would give the maximum revenue is $22.50.
Mrs. Parkes plans to increase the price of her lotion bottles. It currently costs $20.00 and she has 1000 people who purchase the lotion. Each time she increases the price by $0.50, twenty fewer persons will buy the lotion bottles. She has stated that an equation that models the revenue
is y = (20 + 0.5x)(1000 - 20x). Determine the maximum amount of money made? If 20+0.5x represents the new price of the lotion, based on the value of x in the vertex, what is the new price that would give the maximum revenue?
1 answer
1 answer