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. (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. $

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose a company has fixed costs of $36,000 and variable cost per unit of
1
3
x + 222 dollars,
where x is the total number of units produced. Suppose further that the selling price of its product is
1,452 − 
2
3
x 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?
$
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