MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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 [tex]x[/tex] 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:[tex]\text{Revenue} = \text{Price}\times \text{Quantity} = \$\;28x[/tex].Paula's cost comes in two parts:[tex]\begin{aligned}\text{Cost} = \text{Total Cost}&= \text{Fixed Cost} + \text{Marginal Cost}\\ & = \$\;12,000 +\$\; 4x \\ & = \$\;(12,000 + 4x)\end{aligned}[/tex].Consider the inequality in the picture:[tex]\text{Revenue} - \text{Cost} \ge \text{Profit}\\ \$\; 28x - \$\; (12,000 + 4x)\ge 48,000\\\$\; 24x \ge 60,000[/tex].Multiply both sides with 1/24. It is important that this number is positive. Otherwise, the direction of the inequality operator will flip.[tex]\displaystyle x \ge \frac{\$\;60,000}{\$\; 24}[/tex].[tex]x\ge 2,500[/tex].In other words, Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.