If a consumer has a budget of $100 and wants to maximize their utility by purchasing two goods, X and Y, where the price of X is $20 and the price of Y is $10, how many units of each good can they purchase to achieve maximum utility?

To maximize utility with a budget of $100 while buying goods X and Y, we need to consider the prices of both goods. The price of good X is $20, so if a consumer buys 0 units of Y, they can buy 5 units of X (100 divided by 20). Conversely, if they buy only good Y at $10 each, they can purchase 10 units (100 divided by 10). To find the best combination, the consumer can buy 4 units of X for $80 and 2 units of Y for $20, using the entire budget and balancing their spending. This combination allows the consumer to enjoy both goods while utilizing their budget fully, which is key to maximizing their overall satisfaction or utility.