Question

Bernardo spent $15 on supplies for his lemonade stand. He charees $1.25 per giass. The function P(x)=1.25x-15 represents his profit, where x is the number of thasses of lemonade sold.

Answer 1

Bernardo's profit function is P(x) = 1.25x - 15, where x is the number of glasses of lemonade sold. He must sell at least 12 glasses to recover his $15 investment and to start making a profit.

Step-by-step explanation:

The profit function P(x) = 1.25x - 15 represents Bernardo's profit from his lemonade stand, with x representing the number of glasses sold. To achieve a profit, Bernardo needs to sell enough glasses of lemonade to cover his initial expense of $15. The break-even point can be found when P(x) is equal to zero; this is when total revenue from sales equals the cost of supplies. To determine how many glasses he needs to sell to start making a profit, we set the profit equation to zero:

0 = 1.25x - 15

Adding $15 to both sides gives us:

1.25x = 15

Dividing both sides by $1.25:

x = 12

This means that Bernardo needs to sell at least 12 glasses of lemonade to recover his initial $15 investment. Any sales beyond 12 glasses will result in a profit.