Question

An advertiser is charged $31 for 100 copies of a flyer and $47 for 283 copies of another flyer. The printer charges a fixed set-up cost plus a charge for every copy of the flyer. Find a function that describes the cost of a printing job, if n is the number of copies made. C(n) = ?

Answer 1

To find the cost function, we set up a linear equation using the given data points and solve for the fixed and variable costs, which when found, give us the desired cost function C(n).

Step-by-step explanation:

The student is asking about finding a function that describes the cost of a printing job, given fixed and variable costs. We have two points representing the cost for different numbers of copies: ($31, 100) and ($47, 283). We can assume that the cost function is linear, which can be written in the form C(n) = a + bn, where a is the fixed cost, and b is the variable cost per copy.

To find 'a' and 'b', we can set up two equations using the given points:

• 31 = a + 100b
• 47 = a + 283b

By solving this system of equations, we find the fixed and variable costs, 'a' and 'b', and construct the function C(n) accordingly. Finally, we get the cost function that will calculate the total cost for any number of copies 'n'.