Question

11. A company plans to have coffee mugs produced with the company logo on them. The cost of each

depends on the number of mugs that are ordered and is modeled by y =
0.0001x2 0.1x + 30, where x
is the number of mugs ordered and y is the cost (in dollars). What is the minimum cost of each mug?

Answer 1

$5

Explanation:

The cost of each mug depends on the number of mugs that are ordered and is modeled by :

`y =0.0001x^2+ 0.1x + 30` ...(1)

We need to find the minimum cost of each mug.

For minimum cost, dy/dx = 0

So,

`(d(0.0001x^2- 0.1x + 30))/(dx)=0\\\\2x(0.0001)-0.1=0\\\\0.0002x=0.1\\\\x=(0.1)/(0.0002)\\\\x=500`

Put the value of x in equation (1).

`y =0.0001(500)^2- 0.1(500) + 30\\\\y=5`

So, the minimum cost of each mug is $5.