Piecewise Function

Question

A club is asking a company to print shirts.

The quoted price is as follows:

 

set up fee: $50

first 50 shirts are $7.99 each

any additional shirts are $6.99 each.

 

Find a formula for the piecewise function that represents the total cost of ordering n shirts from the company. How much would it cost to order 500 shirts.

Answer 1

For  n < 50    (This should be a less than or equal to sign)
                         C (n) = 7.99 n + 50

For  n > 50            C (n) = 6.99 (n-50) + 449.50
           (The 449.50 amount is 50 + 7.99(50))
            which is  C (n) = 6.99 n + 100

Cost of 500 shirts (n=500)  is   C (500) = 6.99 (500) + 100 =  3595