The cost \( C \) (in dollars) of producing \( x \) widgets in represented by \( C=4.5 x^{2} \). How many widget re produced if the cost is \( \$ 544.50 \) ?

To find out how many widgets are produced for the cost of \$544.50, you can set the equation equal to the cost: \[ 4.5x^2 = 544.50 \] Dividing both sides by 4.5 gives: \[ x^2 = \frac{544.50}{4.5} = 121 \] Taking the square root of both sides, we find: \[ x = 11 \] So, 11 widgets are produced when the cost is \$544.50! To get into the specifics, this formulation reflects a common scenario in manufacturing. The cost function \( C = 4.5x^2 \) indicates that as production increases, costs rise quadratically due to factors like labor and materials becoming more efficient, but also potentially more expensive at scale. It’s a classic economic case where you might want to optimize production levels! To ensure you avoid common pitfalls, double-check your calculations, especially during division and square root extraction. Quadratic equations can be tricky if you overlook a sign or make a miscalculation. Always verify that your answer fits within logical production constraints, such as operational limits and resource availability!