Profit. The financial department for the company in Problems 86 and 88 established the following cost function for producing and selling x thousand notebook computers: C x = 4 , 000 + 500 x thousand dollars (a) Write a profit function for producing and selling x thousand notebook computers and indicate its domain. (b) Complete Table 13 , computing profits to the nearest thousand dollars. (c) Plot the points in part (B) and sketch a graph of the profit function using these points.
Profit. The financial department for the company in Problems 86 and 88 established the following cost function for producing and selling x thousand notebook computers: C x = 4 , 000 + 500 x thousand dollars (a) Write a profit function for producing and selling x thousand notebook computers and indicate its domain. (b) Complete Table 13 , computing profits to the nearest thousand dollars. (c) Plot the points in part (B) and sketch a graph of the profit function using these points.
Solution Summary: The author calculates the profit function and its domain, if the price demand and the cost function are p(x)=2000-60x,1le
Profit. The financial department for the company in Problems
86
and
88
established the following cost function for producing and selling
x
thousand notebook computers:
C
x
=
4
,
000
+
500
x
thousand dollars
(a) Write a profit function for producing and selling
x
thousand notebook computers and indicate its domain.
(b) Complete Table
13
, computing profits to the nearest thousand dollars.
(c) Plot the points in part (B) and sketch a graph of the profit function using these points.
A certain cost function has the following graph:
8,000
6,000
4,000
2,000
0.
50
100
150
200
Items
Dollars
The total revenue function for a product is given by
R = 540x dollars, and the total cost function for this same
product is given by C = 13,500+ 60x + x², where C is
measured in dollars. For both functions, the input x is the
number of units produced and sold.
a. Form the profit function for this product from the two
given functions.
b. What is the profit when 24 units are produced
and sold?
c. What is the profit when 38 units are produced
and sold?
d. How many units must be sold to break even on
this product?
(・・・)))
a. Write the profit function.
P(x) =
(Simplify your answer.)
b. When 24 units are produced and sold, there is
a
of $.
(Simplify your answer.)
c. When 38 units are produced and sold, there is
of $.
a
(Simplify your answer.)
d. The number of units that must be sold to break
even on this product is.
(Simplify your answer. Use a comma to separate
answers as needed.)
If x represents the number of items produced, (a) write a cost function, (b) find a revenue function if each item sells for the price given, (c)
state the profit function, (d) determine analytically how many items must be produced before a profit is realized (assume whole numbers of
items), and (e) support the results of part (d) graphically.
The fixed cost is $600, the cost to produce an item is $25, and the selling price of the item is $50.
(a) The cost function is C(x) =
(Simplify your answer. Do not factor.)
(b) The revenue function is R(x)=
(Simplify your answer. Do not factor.)
(c) The profit function is P(x) =
(Simplify your answer. Do not factor.)
←
(d) At least items must be produced before a profit is shown.
(Type a whole number.)
(e) Choose the correct graph to the right.
O A.
2100
O C.
Dollars
Items produced
2100
Items produced
Q
O B.
2100
O D.
Dollars
2100
Items produced
Items produced
Q
✔
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Mathematical Ideas (13th Edition) - Standalone book
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