Question

A manufacturer of mountain bikes has found that when 20 bikes are produced per day, the average cost is $200 and the marginal cost is $150. Based on the information, approximate the total cost of producing 21 bikes per day.

Answer 1

If the average cost is 200 per 20 bikes, the total cost for 20 bikes is: 200 * 20

Then you have to add another bike, which has a marginal cost of 150

so it's 200 * 20 + 150

Answer 2

The manufacturer of a product has found that when 20 units are produced per day, the average cost is $150 and the marginal cost is $125. What is the relative rate of change of the average cost with respect to quantity when q=20?

How would i set up the equation? I know how to differentiate and find relative rate of change... but I get lost when trying to generate an equation.

Answer 3

Hmmm.

Total cost = Average Cost * Quantity

Marginal cost (Change in total cost) = Average cost * Change in quanity + Change in average * Quanity

125 = 200 * 0 + 20 * Change in average cost

125/20 = change in average cost.

Actually, I have no Idea how to do this, I did economics a year ago. But maybe this helps?

Answer 4

Although this should be negative, since the average cost will decrease when the marginal cost is lower than the average cost.

Answer 5

the answer in the book says -1/120

Answer 6

I agree, it's just frustrating trying to generate an equation :P but the relationships helped, thanks :)

Answer 7

I disagree with your book. -1/120 is way too small :/

Answer 8

maybe it is wrong, i am more concerned with figuring out how to write the equation... math exam in a few weeks!

Answer 9

average cost per unit:
C = c/q where c is cost and q is quantity

Answer 10

oh wait

Answer 11

if you isolate for c (cost), you get Cq = c or 150*20 = 3000?

Answer 12

Everything starts with this formula:

TC = AC * Q

Deriving this:

dTC/dQ = dAC/dQ * Q + A(dQ/dQ)

dTc/dQ = Marginal cost

Marginal cost = Q * dAc/dQ + A

125 = 20 * dAc/dQ + 150

-25 = 20 * dAc/dQ

-25/20 = dAC/dQ

So the answer is -5/4

Answer 13

total cost = average cost * quantity? just to clarify

Answer 14

Yes

Answer 15

and what is A?

Answer 16

Sorry, meant Average cost

Answer 17

perfect, i will try to work through this using that formula, and consult my TA about it when we return to classes on Monday :) thanks so much

Answer 18

Cool, no problem. Just remember, try writing the basic formulas and then deriving those.

Key points to know:

Total cost = Average Cost * Quantity

Marginal cost = Change in total cost = dTC/dQ