Suppose a company has fixed costs of $33,800 and variable cost per unit of $\frac{1}{3}x + 222$ dollars, where $x$ is the total number of units produced. Suppose further that the selling price of its product is $1548 - \frac{2}{3}x$ dollars per unit.
(a) Form the cost function and revenue function (in dollars).
$C(x) = \frac{1}{3}x + 34022$
$R(x) = 1548x - \frac{2}{3}x^2$
Find the break-even points. (Enter your answers as a comma-separated list.)
x = 2299,22
(b) Find the vertex of the revenue function.
$(x, y) = (1161, 898614)$
Identify the maximum revenue.
$ 898614
(c) Form the profit function from the cost and revenue functions (in dollars).
$P(x) = -\frac{2}{3}x^2 + \frac{4643}{3}x - 34022$
Find the vertex of the profit function.
$(x, y) = (1160, 864205)$
Identify the maximum profit.
$ 864205
(d) What price will maximize the profit?
$ .05
