Question

The total cost of developing and manufacturing a brand of cosmetics takes the form TC=0.05Q^3+aQ^2+110Q+b The fixed development and production costs are ​$7,000. Find the minimum average cost if it is known that this occurs at Q​ = 80. ​(Give your answer to the nearest​ dollar.)

The minimum average cost is $ ?

Answer 1

Here b is the fixed cost which is given b=$7000

Now to find out the average cost we need to devide the total cost by Quantity Q.

minimum average cost:

we know that it occurs at Q=80 so lets find out a:

Thus the minimum average cost will be:

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Minimum Average cost is $1070