Question 1096736
the linear cost function is y = 200,000 + 200 * x


the average cost function is y = (200,000 + 200 * x) / x


the horizontal asymptote of the average cost function is 200.


as the number of bikes sold becomes greater and greater, the effect of the fixed cost becomes less and less until it becomes almost 0, at which time you are effectively dealing with the incremental cost of production only.


c(x) = 200,000 + 200 * x.


that's your cost function.


when you set y = c(x), they mean the same thing.


y = 200,000 + 200 * x is the same equation as c(x) = 200,000 + 200 * x.


when you sell 1 bike, the average cost is (200,000 + 200 * 1) / 1 = 200,200.


when you sell 1,000,000 bikes, the average cost is (200,000 + 200 * 1,000,000) / 1,000,000) = 200.2 per bike.


when you sell 1,000,000,000 bikes, the average cost is (200,000 + 200 * 1,000,000,000) / 1,000,000,000 = 200.0002


of course, this is highly theoretical because nobody sells 1,000,000,000 bikes each month.


not that i know of, anyway.


however, the average cost of a bike sold gets closer and closer to the incremental cost of 200, the more bikes you sell in a month.