Question

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

Answer 1

Step-by-step explanation:

Since we are not given the cost function, let the cost function be expressed as C(x) = 0.2x²-2.6x+9.950

where​ C(x) is in hundreds of dollars.

x is the number of bicycle built

In order to minimize the average cost of the bicycle, then d(C(x))/dx = 0

d(C(x))/dx = 2(0.2)x²⁻¹ - 2.6

d(C(x))/dx = 2(0.2)x- 2.6

d(C(x))/dx = 0.4x- 2.6

Since d(C(x))/dx =0, then;

0.4x - 2.6 = 0

0.4x = 2.6

x = 2.6/0.4

x = 6.5

Hence around 6 bicycles should be built by the shop to minimize the average cost per​ bicycle