J's bike has determined that when x hundred bikes are built, the average cost per bike is given by C(x)= 0.1x^2-1.2x+4.993, where C(x) is in hundreds of dollars. how many bikes should the shop build to minimize the average cost per bike?

Answer 1

Differentiate cost function and equate it to 0, i.e. 0.1(2x)-1.2=0 or x=1.2/0.2=6; Second derivative is0.2which is+ve hence it corresponds to minimum cost level. Hence x=6,i.e. 600 bikes.
Cost/bike for 600 bikes will be
=0.1x36-1.2x6+4.993=1.393 hunderd $.
For 590 and 610 bikes put x=5.9 and6.1 and calculate the cost; it comes to 1.394 in each case which is>that for x=6.