The manager of a restaurant found that the cost to produce 200 cups of coffee is $20.95, while the cost to produce 500 cups is $50.35. Assume the cost C(x) is a linear function of x, the number of cups produced. Answer parts a through f.

a. Find a formula for C(x)
b. What is the fixed cost
c. Find the total cost of producing 1200 cups
d. Find the total cost of producing 1201 cups
e. Find the marginal cost of the 1201st cup
f. What is the marginal cost of any cup and what does this mean to the manager