Final answer:
To ensure that the average cost per item does not exceed $20, the firm must produce at least 25 items as determined by the cost function C(x) = -5x + 625.
Step-by-step explanation:
The given function C(x) = -5x + 625 represents the cost to produce x items. To find the least number of items that can be produced so that the average cost is no more than $20, we need to set up the average cost equation: average cost = C(x) / x. Thus, we have:
20 ≥ C(x) / x
20 ≥ (-5x + 625) / x
Multiplying both sides by x (assuming x is not zero) and rearranging gives:
20x ≥ -5x + 625
25x ≥ 625
x ≥ 625 / 25
x ≥ 25
Therefore, the firm must produce at least 25 items to ensure that the average cost per item is no more than $20.