Question

Will mark the brainliest.

Paula makes stained-glass windows and sells them to boutique stores. If her costs total $12,000 per year plus $4 per window for the frame. How many windows must she produce to earn a profit of at least $48,000 in one year if she sells the windows for $28 each?

Answer 1

Answer:

Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.

Step-by-step explanation:

Let $x$ be the number of windows that Paula sells in a year.

Paula's revenue is the number of windows that she sell times the price that she charge for each window. That is:

$\text{Revenue} = \text{Price}\times \text{Quantity} = \ \;28x$.

Paula's cost comes in two parts:

$\begin{aligned}\text{Cost} = \text{Total Cost}&= \text{Fixed Cost} + \text{Marginal Cost}\\ & = \ \;12,000 +\ \; 4x \\ & = \ \;(12,000 + 4x)\end{aligned}$.

Consider the inequality in the picture:

$\text{Revenue} - \text{Cost} \ge \text{Profit}\\ \ \; 28x - \ \; (12,000 + 4x)\ge 48,000\\\ \; 24x \ge 60,000$.

Multiply both sides with 1/24. It is important that this number is positive. Otherwise, the direction of the inequality operator will flip.

$\displaystyle x \ge \frac{\ \;60,000}{\ \; 24}$.

$x\ge 2,500$.

In other words, Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.