He purchased $12.00 worth of lemons and $4.00 worth of glasses to make the lemonade.

He adds $0.02 worth of sugar to each glass of lemonade.

He sells each glass of lemonade for $0.25.

What is the minimum number of glasses of lemonade that Michael needs to sell to begin to make a profit?

The minimum number of glasses of lemonade is 70

Step-by-step explanation:

Equations

With the data provided, we can build a model for the profit that Michael gets for selling lemonade.

First, we set up the cost function. He purchased $12 in lemons and $4 in glasses. It makes a fixed cost of $16. He also spends $0.02 per glass of lemonade fot the sugar. Being x the number of glasses of lemonade Michael sells, the total cost is modeled by

C (x) = 16+0.02x

The revenue for selling x glasses of lemonade is

R (x) = 0.25x

The profit is

P (x) = R (x) - C (x) = 0.25x - (16+0.02x)

P (x) = 0.23x-16

To make profits:

0.23x-16>0

Solving for x

x>16/0.23

x>69.6

Since x must be an integer

The minimum number of glasses of lemonade is 70