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# 2. Functions from Verbal Statements

### Example 1

When operating a factory, there are fixed costs like electricity, labor and storage space. One such factory has fixed costs of $50,000 per day. There are also variable costs, for example, if they make more widgets it will cost more in materials, extra labor costs and extra power costs. The factory calculates there is a variable cost of $10 to manufacture each extra widget.

Write the daily cost C as a function of the number of units produced.

Answer

Let's say the factory produces x widgets per day. (We could choose any meaningful variable - n would also be a good choice.)

The daily total cost C equals the fixed cost of $50,000 plus the variable cost of producing x units. The cost of producing 1 unit is $10, so the cost of producing x units is $10x. So the total cost C, where C is a function of x is C(x) = 50000 + 10x  For example, the daily cost of making 2000 widgets is: C(2000)  = 50000 + 10 × 2000  =$70,000

Note that in this example, x can only take integer values of 0 or more (we can't make negative widgets).