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?

$5

Step-by-step explanation:

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

...(1)

We need to find the minimum cost of each mug.

For minimum cost, dy/dx = 0

So,

Put the value of x in equation (1).

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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions