Suppose a company has fixed costs of $36,000 and variable cost per unit of
1/3x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1,452 −2/3x dollars per unit.

Form the cost function and revenue function (in dollars).
C(x)=
R(x)=

Find the break-even points. (Enter your answers as a comma-separated list.)
x =

Find the vertex of the revenue function.
(x, y) =

Identify the maximum revenue.

Form the profit function from the cost and revenue functions (in dollars).
P(x) =

Find the vertex of the profit function.
(x, y) =

Identify the maximum profit.

What price will maximize the profit?