The cost function for a product is C(x)=0

The way this question is worded is a little unclear. Is the cost function defined only over the domain x∈[0,350]x∈[0,350]? Do they want a general function over it? Or do they want the average cost when we produce x=350x=350 items? Beats me, so we'll get both.

The average cost function is

¯C(x)=0.8x2+130x+160x=0.8x+130+160xC¯(x)=0.8x2+130x+160x=0.8x+130+160x

So if we produce 350 items, then the average cost is

¯C(350)=0.8(350)+130+160350≈$410.46C¯(350)=0.8(350)+130+160350≈$410.46

Average Cost:

Recall that the average cost is the average cost to produce each item or good. So to compute it, we need to divide the total cost by the number of items produced. But the number of items produced is simply xx, and so the average cost function is the total cost divided by xx:

¯C(x)=C(x)x