Question

The cost in dollars to produce x cups of lemonade is represented by the function C(x) = 10 + 0.20x. The revenue in dollars earned by selling x cups of lemonade is represented by the function R(x) = 0.50x. What is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?

Answer 1

Revenue > Cost
R(x) > C(x)
0.50x > 10+0.20x
0.50x-0.20x > 10
0.30x > 10
x > 10/0.30
x > 33.333 which is approximate

Round up to the nearest whole number to get x = 34. You need to sell at least 34 cups of lemonade to have the revenue R(x) be larger than the cost C(x)

Answer: 34