Algebra
posted by pj on .
Aki's Bicycle designs has determined that when x hundred bicyles are built, the average cost per bicycle is given by C(x)=0.6^20.5x+4.021, where C(x) is in hundreds of dollars. How many biccles should the shop build to minimize the average cost per bicycle?
The shop should build _____ bicycles.
Could you please help me!!!!

Don't you mean
C(x)=0.6 x^2  0.5x + 4.021 ?
I think you left out an x.
Since you are not taking calculus, I will assume that you are supposed to answer this question by turning C(x) into a "perfect square" plus a constant.
C(x)= 0.6 x^2  0.5x + 4.021
0.6 [x^2  (5/6)x + (5/12)^2] + 3.916
= 0.6(x  5/12)^2 + 3.916
This is a minimum when x = 5/12. that means the number of bicyles is (5/12)*100 = 41.7
Pick x = 0.42 instead of 0.41, since it is closer to 5/12 and 100x must be an integer.
Proof: If x = 0.41, C(x) = 3.91686
if x = 0.42, C(x) = 3.91684
if x = 0.43, C(x) = 3.91694