Question

April sells specialty teddy bears at various summer festivals. Her profit for a week, P, in dollars, can be modelled by P= -0.1n^2 + 30n - 1200, where n is the number of teddy bears she sells during the week.

1) according to this model , could April ever earn a profit if $2000 in one week? Explain.

Answer 1

April cannot earn a $2000 profit in one week by selling teddy bears according to the model P = -0.1n^2 + 30n - 1200, since the quadratic equation returns complex numbers, indicating that there are no real solutions for n that would result in a $2000 profit.

Step-by-step explanation:

The question asks whether April can earn a profit of $2000 in one week by selling specialty teddy bears according to the model P = -0.1n2 + 30n - 1200, where P represents the profit and n is the number of teddy bears sold. To determine this, we need to find if there is a value for n that makes P equal to 2000.

Let's set up the equation with P equal to 2000:

1. -0.1n2 + 30n - 1200 = 2000
2. Simplify the equation to -0.1n2 + 30n - 3200 = 0.
3. Use the quadratic formula to solve for n:

n = (-b ± √(b2 - 4ac)) / (2a), where a = -0.1, b = 30, and c = -3200.

By applying the quadratic formula, we can find the possible number of teddy bears April needs to sell to achieve a $2000 profit. Unfortunately, the quadratic formula returns complex numbers, which means there are no real solutions. Therefore, according to the given model, April cannot earn a $2000 profit in one week.