A company sells a luxury anti-aging cream, the total cost of producing one bottle is given by the function C(x) = 2350 + 80x - 0.04x² and that the demand for the cream is given by the equation = /2 + 17.5

where p is the price per bottle

a) Express the price p as a function of the demand x, and find the domain of this function.

b) Find the marginal cost.

c) Find the revenue function and state its domain.

d) Find the marginal revenue.

e) Find the profit function in terms of x.

f) Find the marginal profit.