The total cost, C, in dollars, of operating a factory that produces kitchen utensils is (x)=0.5x^2+40x+8000, where x is the number of items produced, in thousands. Determine the rate of change of the average cost of producing 5000 times. Interpret this value.

Question

istim · Answer

No work done.

istim · Answer

Average cost is $1.64.

anonymous · Answer

Woah. This is something different. Hmm. when u say average cost is 1.64 meaning that is part of the questions. or u worked it out?

istim · Answer

Worked it out.

istim · Answer

I did this from dividing the total cost by the number of items produced.

anonymous · Answer

Hmm i think this questions has a bit of problem in it. Cause it asks for the rate of change of the cost of producing 5000 items. That means you have to take into account the time taken to produce 1 item, which you cannot find given the limited information given in the question. Note: Rate always involves time. So now i have not a clue what the question really wants. Cant really help =x

istim · Answer

I have determined the marginal cost of producing 50000 items, and cost of producing 5001st item. Would that help?
The rate is also related to the derivative, if that helps with anything. Actually, This have given me a iddea. With the Cost function's derivative help?

anonymous · Answer

Okay looking at your reply i got an idea too. First i stand by my point, using the term 'rate' here is wrong and just serve to confuse. WHat i think the question is getting at is the marginal cost of producing one more item in addition to the 5000 items.

istim · Answer

Whoops, 5000, not 50 000

anonymous · Answer

Given (x)=0.5x^2+40x+8000. as the formula for total cost.

By differentiating it, you will get the marginal costs
Marginal cost, MC = x+40

Substitute x = 5, (Note the questions state that x is the number of items produced in thousands, so is 5 instead of 5000)

MC = 5+40 =$45

intepreting it in words,

$45 is the additional cost of producing the 5000st unit.