College Algebra

Question

Aki’s Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycles is given by C(x)= 0.1x^2-1.3x+10.533, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

The shop should should build ____ bicycle.

Answer 1

Total Cost = Average Cost times x = C(x)x = .1x^3 -1.3x^2 + 10.533x

Marginal Cost = the derivative of Total Cost = .3x^2 - 2.6x + 10.533

set Marginal Cost = Average Cost. Graphically they intersect at the minimum Average Cost

.3x^2 - 2.6x + 10.533 = .1x^2 - 1.3x + 10.533

.2x^2 - 1.3x = 0

2x^2 -13x = 0

x(2x -13) = 0

2x-13 = 0

x = 13/2 = 6.5 hundred = 650 bicyles

C(6.5) = .1(6.5)^2 - 1.3(6.5) + 10.533 = 4.225 - 8.45 + 10.533 = 6.308 = $630.8 = minimum Average Cost