Expert: Scotto - 7/21/2008

Question
Hi Mr. Scotto.

I am having trouble with a problem, please help me with this:

Question: "Average cost"

A manufacturer incurs the following costs in producing x blenders in one day for 0<x<200: fixed costs $450, unit production cost, $30 per blender, equipment maintenance and repairs 0.08x2(0.08 X SQUARE) dollars.

(A) What is the average cost C_(X) per blender if x blenders are produced in one day ?

(B) Find the critical values of C_(X), the intervals on which the average cost per blender is decreasing, the intervals on which the average cost per blender is increasing, and the local extrema. Also Graph it.

Along with the solution, can you also explain how do we find the C_(X) cost function with the given values?

Thanks A lot.
Bilal

Answer
C(x)=450+30x+0.08x²

(A) To find the average, integrate C(x) from the minimum number to the maximum number.  It would be the difference in 450x+15x²-0.08x^3/3 between x=200 and x=0.  At zero, the function is 0.  At 200, the value is 450(200) + 15(200²) - 0.08(200^3)/3.

(B) Setting the derivative equal to 0 to find the critical points, you would get x=187.5, so use the closest integers for the solutions would be x=187 or x=188.  At both of these points, the profit is found to be 3,212.

To evaluate C(x), put in the values x=187 and x=188.

The cost function was given at the topof the respons

The 450 is the base value we always spend.  the 30x is for the fact there is a cost of 30 for each one. The point 0.08x² they told us to subtract off as well.