Question

Aki's Bicycle Designs has determined that when x hundred bicycles are​ built, the average cost per bicycle is given by​ C(x)equals=0.50.5xsquared2minus−0.20.2xplus+6.7566.756​, where​ C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per​ bicycle?

Answer 1

20 Bicycles

Explanation:

The function for the average cost,C(x) [in hundred of dollars] per bicycle whenever x hundred bicycles are built is given as:

`C(x)=0.5x^2-0.2x+6.756`

The minimum value of C occurs at the axis of symmetry.

Axis of Symmetry,
`x=-(b)/(2a)`

Comparing with the standard form of a quadratic equation
`ax^2+bx+c=0`

a=0.5, b=-0.2

`x=-((-0.2))/(2*0.5)\\x=0.2`

x=0.2 Hundreds =0.2 X 100 =20

When Aki's Bicycle Designs produces 20 Bicycles, the cost is minimized.