Carrie is considering three different types of materials for her chairs. depending on the price she sets for each chair, the costs and revenues for each type of material will generate different costs and revenues for her business.

in the functions, x is the price of each chair. the functions give the revenue (r) and costs (c) that carrie’s business can expect in a year at a given price for the item. select the correct answer

material 1
r(x) = 200,000x - 2,000x2
c(x) = 5,000,000 - 20,000x

material 2
r(x) = 160,000x - 1,000x2
c(x) = 4,000,000 - 10,000x

material 3
r(x) = 54,000x - 270x2
c(x) = 2,000,000 - 5,000x

the highest profit is
a. 500,000
b. 2,055,000
c. 3,225,000
d. 4,125,000

which material can deliver the highest profit
a. material 1
b. material 2
c. material 3

material profit for the widest range of prices.