An online seller of T-shirts pays $\$ 500$ to start up the website and $\$ 8$ per T-shirt, then sells the T-shirts for $\$ 11$ each. Give the cost, revenue, and profit functions in terms of $q$, the number of shirts sold.

Step 1 ：Given the startup cost is \(\$500\) and the cost per T-shirt is \(\$8\), the cost function is C(q) = 500 + 8q

Step 2 ：Since the seller sells each T-shirt for \(\$11\), the revenue function is R(q) = 11q

Step 3 ：The profit function is the difference between the revenue and the cost, so P(q) = R(q) - C(q)

Step 4 ：Calculating the profit function: P(q) = (11q) - (500 + 8q)

Step 5 ：Simplifying the profit function: P(q) = 3q - 500

Step 6 ：\(\boxed{\text{Cost function: } C(q) = 500 + 8q, \text{ Revenue function: } R(q) = 11q, \text{ Profit function: } P(q) = 3q - 500}\)