Question

3

Work: Mia sells used MP3 players. The average cost to package MP3 players is given by the
equation, c(x) = 2x2 – 40x + 2200, where x is the number of MP3 players she packages
in a week. How many players must she package to minimize her average cost?

Answer 1

Given:

The average cost of MP3 players.

`c(x)=2x^2-40x+2200`

where x is the number of MP3 players.

To get the number of MP3 players she needs to pack to minimize her cost, we differentiate the equation and equate the differential to zero, and solve for x.

`\begin{gathered} c(x)=2x^2-40x+2200 \\ c^1(x)=4x-40 \end{gathered}`

Hence,

`\begin{gathered} To\text{ minimize her cost,} \\ c^1(x)=0 \\ \text{Thus,} \\ 4x-40=0 \\ \text{Collecting the like terms,} \\ 4x=0+40 \\ 4x=40 \\ \text{Dividing both sides by 4,} \\ x=(40)/(4) \\ x=10 \end{gathered}`

Hence, Mia must package 10 MP3 players to minimize her average cost.