Answer:
$5
Step-by-step explanation:
The cost of each mug depends on the number of mugs that are ordered and is modeled by :
[tex]y =0.0001x^2+ 0.1x + 30[/tex] ...(1)
We need to find the minimum cost of each mug.
For minimum cost, dy/dx = 0
So,
[tex]\dfrac{d(0.0001x^2- 0.1x + 30)}{dx}=0\\\\2x(0.0001)-0.1=0\\\\0.0002x=0.1\\\\x=\dfrac{0.1}{0.0002}\\\\x=500[/tex]
Put the value of x in equation (1).
[tex]y =0.0001(500)^2- 0.1(500) + 30\\\\y=5[/tex]
So, the minimum cost of each mug is $5.
