Amys bicycle designs has determined that when x hundred bicy

Amy\'s bicycle designs has determined that when x hundred bicycles are built the average cost per bicycle is given by
C ( x) = 0.5x^2 -0.8 x + 5.648 where C ( x) is in the hundreds of dollars. How many bicycles should the shop build to minimize the average cost for a bicycle?

The Shop should build ____ bicycles.

Solution

Given :

c(x) = 0.5x² - 0.8x + 5.648

Differentiate cost function and equate it to 0, we get:

1(x) - 0.8(1) + 0 = 0

x - 0.8 = 0

or, x = 0.8

Second derivative is 1 which is +ve.

Hence it corresponds to minimum cost level.

Hence x = 0.8

when x hundred bicycles are built then = 0.8 * 100

= 80 bicycles

Cost per bicycle for 80 bicycle will be :

plug x = 0.8 into c(x) , we get:

= 0.5 ( 0.8)² - 0.8 ( 0.8 ) + 5.648

= 5.328 hundred $