SOLUTION: Suppose a ceiling fan manufacturer has the total cost function C(x) = 37x + 2280 and the total revenue function R(x) = 75x. (a) What is the equation of the profit function P

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Question 1204313: Suppose a ceiling fan manufacturer has the total cost function
C(x) = 37x + 2280
and the total revenue function
R(x) = 75x.
(a) What is the equation of the profit function P(x) for this commodity?
P(x) =

(b) What is the profit on 40 units?
P(40) =

Interpret your result.
The total costs are less than the revenue.
The total costs are more than the revenue.
The total costs are exactly the same as the revenue.
(c) How many fans must be sold to avoid losing money?
fans
Answer by mananth(16946) (Show Source):
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Suppose a ceiling fan manufacturer has the total cost function
C(x) = 37x + 2280
and the total revenue function
R(x) = 75x.
(a) What is the equation of the profit function P(x) for this commodity?
P(x) =
(b) What is the profit on 40 units?
P(40) =
Interpret your result.
The total costs are less than the revenue.
The total costs are more than the revenue.
The total costs are exactly the same as the revenue.
(c) How many fans must be sold to avoid losing money?
Profit function P(x):
P(x) = R(x) - C(x)
P(x) = 75x - (37x + 2280)
P(x) = 75x - 37x - 2280
P(x) = 38x - 2280

profit on 40 units
plug x =40
P(x) = 38x - 2280
=40*(38)-2280
= 1520-2280
=-760
P(x)=-760
The company is incurring a loss of $760 when they produce and sell 40 fans. The total costs are greater than the total revenue.
How many fans must be sold to avoid losing money?
C(x)=R(x)
37x + 2280= 75x.
75x-37x =2280
38x =2280
x=60
The company must sell 60 or more than 60 fans to avoid losing money