The cost \( C \) of producing \( x \) thousand calculators is given by the equation below. \[ C=-6.8 x^{2}+7795 x+230,000(x \leq 150) \] The average cost per calculator is the total cost \( C \) divided by the number of calculators produced. Write a rational expression that gives the average cost per calculator when \( x \) thou produced. The rational expression for the average cost is (Do not simplity.)

To find the average cost per calculator, we start with the total cost \( C \) and divide it by the total number of calculators produced, which is \( 1000x \) (since \( x \) is in thousands). Thus, the average cost \( A \) is given by: \[ A = \frac{C}{\text{number of calculators}} = \frac{-6.8x^2 + 7795x + 230000}{1000x} \] So the rational expression for the average cost per calculator when \( x \) thousand calculators are produced is: \[ A = \frac{-6.8x^2 + 7795x + 230000}{1000x} \] --- Delving into the fascinating world of calculators, it might surprise you to know that the first electronic calculators appeared in the 1960s and were far from portable! The early models were more like small computers, housed in hefty casings and weighing up to several kilograms. Today, we carry powerful calculators in our pockets with smartphones! When calculating costs, a common mistake is overlooking fixed costs—those unavoidable expenses that don’t change with the number of units produced. Always break down costs into fixed and variable components for accurate calculations. Remember, understanding your cost structure can significantly improve pricing strategies and profit margins.