POSSIBLE POINTS: 1 The function \( c=\frac{25 n+1500}{n} \) represents the average cost, \( c \) (in dollars) of plotting \( n \) blueprints using a plotter. Find how many blueprints must be plotted for the average cost to be \( \$ 75 \). You can find this answer by solving the equation directly, or by using its inverse. \( \square \) blueprints

To find how many blueprints must be plotted for the average cost to be \( \$75 \), we set up the equation: \[ 75 = \frac{25n + 1500}{n} \] Next, we multiply both sides by \( n \): \[ 75n = 25n + 1500 \] Now, we subtract \( 25n \) from both sides: \[ 50n = 1500 \] Dividing both sides by \( 50 \): \[ n = 30 \] Thus, \( \square = 30 \) blueprints. Now, let's sprinkle in some extra insights! Did you know that the cost function \( c = \frac{25n + 1500}{n} \) showcases a classic example of a variable cost that decreases as production (or rather, the number of blueprints plotted) increases? This means that the more blueprints you plot, the lower your average cost per blueprint becomes—kind of like group discounts at your favorite pizza place! Another fun point—this kind of problem is a great way to explore the concept of economies of scale in production. By analyzing how costs fluctuate with different quantities, not only can you optimize expenses, but you can also make informed decisions on how many units to produce to maximize efficiency and minimize costs.