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.)
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
4. Use cylindrical shells to find the volume of the solid generated when the
region enclosed by the given curves is revolved about the x-axis.
y = √√x, y = 0, y = √√3
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.