For the given cost function C(x) = 14400 + 800x + x^2 find...

Question

For the given cost function C(x) = 14400 + 800x + x^2 find...

1) The cost at the production level 1900

2) The avg cost at the production level 1900

3) The marginal cost at the production level 1900

4) The production level that will minimize the average cost

5) The minimal average cost

This question is from a Calculus I Exercise on Applied Optimization!

Answer 1

4) C=14400+800x+x^2=total Cost

C/x=AC=Average Cost = 14400/x+800+x

take the derivative with respect to x and set = 0, then solve for x

AC'= -14400/x^2 +0+1=0

-14400+x^2=0

x^2=14400

x=sqr14400, ignore x=-120

x= +120 for minimum AC, Average Cost

5) min AC= C'/120=14400/120 +800 +120=1,040

1) C(1900)= 14400+800(1900)+1900^2=14,400+1,520,000+3,610,000=5,144,400

2) AC(1900)= 14400/1900 +800+ 1900=144/19+2700=2,707 11/19

3) MC= C' =800+2x

C'(1900)= 800+2(1800)=4400