Maximum Profit The cost per unit in the production of an MP3 player is $60. The manufacturer charges $90 per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by $0.15 per MP3 player for each unit ordered in excess of 100 (for example, the charge is reduced to $87per MP3 player for an order size of 120). (a) The table shows the profits P (in dollars) for various numbers of units ordered, x . Use the table to estimate the maximum profit. Units, x 130 140 150 160 170 Profit, P 3315 3360 3375 3360 3315 (b) Plot the points ( x, P ) from the table in part (a). Does the relation defined by the ordered pairs represent P as a function of x ? (c) Given that P is a function of x , write the function and determine its domain. ( Note: P = R − C where R is revenue and C is cost.)
Maximum Profit The cost per unit in the production of an MP3 player is $60. The manufacturer charges $90 per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by $0.15 per MP3 player for each unit ordered in excess of 100 (for example, the charge is reduced to $87per MP3 player for an order size of 120). (a) The table shows the profits P (in dollars) for various numbers of units ordered, x . Use the table to estimate the maximum profit. Units, x 130 140 150 160 170 Profit, P 3315 3360 3375 3360 3315 (b) Plot the points ( x, P ) from the table in part (a). Does the relation defined by the ordered pairs represent P as a function of x ? (c) Given that P is a function of x , write the function and determine its domain. ( Note: P = R − C where R is revenue and C is cost.)
Solution Summary: The author explains that a function f is well-defined relation between two variables, such that each and every element in set A is mapped with exactly one element.
Maximum Profit The cost per unit in the production of an MP3 player is $60. The manufacturer charges $90 per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by $0.15 per MP3 player for each unit ordered in excess of 100 (for example, the charge is reduced to $87per MP3 player for an order size of 120).
(a) The table shows the profits P (in dollars) for various numbers of units ordered, x. Use the table to estimate the maximum profit.
Units, x
130
140
150
160
170
Profit, P
3315
3360
3375
3360
3315
(b) Plot the points (x, P) from the table in part (a). Does the relation defined by the ordered pairs represent P as a function of x?
(c) Given that P is a function of x, write the function and determine its domain. (Note:
P
=
R
−
C
where R is revenue and C is cost.)
A wholesale t-shirt manufacturer charges the following prices for t-shirt orders (see the graph):
• You've ordered 40 shirts. How much does your total order cost?
Price Per Shirt
10-
5
10
Cost of T-shirts
20 30 40
Number of Shirts
50
60
70
80 90
|
+
3. (5.7.12) On June 2, 2010 USA Today reported a story from Bloomberg News that said that the total price
tag for the project to build the new F-35 Joint Strike Fighter would be 65% higher than the original $232 billion
estimate. The cost now is estimated to be $382 billion.
The total cost of each plane would be $112.4 million, up 81% from the original $62 million. The cost to
produce each plane would be $92.4 million, about 85% higher than the original estimate of $50 million.
a. Check the arithmetic to see that the three percentage increases reported are correct.
b. Can you explain how the project cost can have increased by just 65% when the overall total per
plane increased by 81% and the construction cost alone increased by almost 85%?
4. (5.7.3) Check that your own GPA from last semester has been computed correctly using the rules in effect at
YSU. If you are in your first semester and don't yet have a GPA, imagine the grades you expect at the end of
this semester and figure…
Question#2
A car is sold for $2280, at a loss of 5% on the cost price. Find the Cost price?
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