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?

For the income to exceed the cost, a minimum of 34 complete cups of lemonade must be sold.

What is inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

The cost in dollars  C(x) = 10 + 0.20x.

The revenue in dollars, R(x) = 0.50x.

For revenue to outpace 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

Hence, For the income to exceed the cost, a minimum of 34 complete cups of lemonade must be sold.

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