Suppose a company has fixed costs of $30,800 and variable cost per unit of 1/3x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is...

Suppose a company has fixed costs of $30,800 and variable cost per unit of

1/3x + 444 dollars,

where
x
is the total number of units produced. Suppose further that the selling price of its product is 1,572 − 2/3x dollars 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?

Jun 03, 2022

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