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

(a)

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=

(b)

Find the vertex of the revenue function.

(x,y) =

Identify the maximum revenue.

$

(c)

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.

$

(d)

What price will maximize the profit?

$