A manufacturer of custom drinking mugs has a fixed setup cost of $1,000 per order plus a variable cost of $1.50 per mug. How many mugs were produced when the total cost was $2, 800?

Let's start by assigning variables to the unknowns in the problem:
Let's say x represents the number of mugs produced.
The fixed setup cost per order is $1,000, which remains constant regardless of the number of mugs produced.
The variable cost per mug is $1.50, meaning that the total variable cost is 1.50x.

The total cost, which includes both the fixed setup cost and the variable cost, is given as $2,800.

Mathematically, we can represent the total cost as:
Total Cost = Fixed Cost + Variable Cost
2800 = 1000 + 1.50x

To find the number of mugs produced (x), we need to isolate x in the equation.

Subtract 1000 from both sides of the equation:
2800 - 1000 = 1.50x

Simplify the left side:
1800 = 1.50x

To isolate x, divide both sides of the equation by 1.50:
\frac{1800}{1.50} = x

Simplify the right side:
x = 1200

Answer: The manufacturer produced 1200 mugs when the total cost was $2,800.