The average cost function is calculated as the cost divided by the quantity produced. To find the average cost function, you need to find the cost function and the quantity produced. Given the cost and revenue functions, we can calculate the quantity produced (x) by setting the revenue equal to the cost:
4x - 0.06x² = 146 + 8.9x
Solving for x, we can find the quantity produced:
3.9x = 292
x = 75
So, the quantity produced is 75 units. The average cost function can now be calculated as:
C(x) / x = (146 + 8.9x) / x
For x = 75,
C(75) / 75 = (146 + 8.9 * 75) / 75 = 146 / 75 + 8.9 = 2 + 8.9 = 10.9