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?
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.