(20 points) James wants to purchase custom-made hats for a charity event he is organizing. He can choose from these two options:

Option A:Pay a set-up fee of $25.00 plus $5.75 per hat

Option B:Pay a set-up fee of $75.00 plus $4.50 per hat

a)Write linear function f(x) that represents the total charge for Option A for x hats.

No work required.

b)State a linear function g(x) that represents the total charge for Option B for x hats.

No work required.

c)James wants to purchase 30 hats for the event. Which option will give him the lower cost? Work or explanation required.

d)For what number of hats is the cost identical for both options? Work required.

e)Fill in the blanks. No work required.

Option B is the cheaper option if _________ than ___________ hats are ordered.